This question pushes lots of buttons for the Jewish community, and I hope that the responses will be helpful to you and to others who will read them.
As a Reconstructionist Jew, I would argue that Judaism comes to us in two ways; by ascent and descent. We are descended with parents who are Jewish (or in the case of liberal branches of Judaism, one parent of either gender with some markers of Jewish identity). We ascend to Judaism by making Jewish choices, and by taking on a Jewish identity. In some ways, descent is about status and ascent is about identity.
According to the Talmud, once a Jew - always a Jew. In Yevamot, a person who is Jewish at marriage but then converts to another religion, their marriage is still considered valid (meaning the person is still Jewish). Additionally, the Shulhan Aruh, a medieval Jewish Law Code, addresses the question of Jewish marriage and says that in the case that you have described, her children would also be Jewish. In that scenario, perhaps they need to do nothing.
However, Judaism is more than a series of rigid rules. Judaism is the civilization of the Jewish people, and so it is ever evolving and responding to the diverse needs of the Jewish community. I would argue that a person who chooses to join another religious tradition loses their Jewish status within the community. They have clearly given up their Jewish identity. If they choose to return later in life, that is wonderful (although not necessarily preferable) and they should go through the rituals of conversion.
There are no special rituals for conversion. The rituals of conversion are things that all Jewish people do at certain times. We might sit in front of a beyt din in case of divorce, or perhaps at other moments of transition. We immerse in the mikvah at regular intervals and also to mark special moments in life - both good and bad. We circumcise all Jewish boys when appropriate and safe. If we really want to get technical about it, the rituals of conversion reflect a transition (from non-Jewish to Jewish) that has already occurred. We are just marking it through normative rituals of Jewish people. That is why there is no specific blessing for conversion.
Because of that, and because the person in question is really trying to reclaim Jewish identity (if not also Jewish status) I would advocate that we require conversion rituals for this person. While other people may disagree, if we think about the Jew standing in front of us rather than the general halahic principle, I believe that in the majority of cases we will find these rituals to be helpful in the reclaiming of identity, and the transition back to the Jewish community.
Since your question is about a “[Jewish] child who converts to Christianity,’ it appears that this is as opposed to a ‘Jewish adult’ who converts. There is an obvious distinction in civil law as with Jewish Law (Halakhah), when speaking about the actions of a child or an adult (a minor or major).
Traditionally speaking, a minor in Judaism is a male under the age of thirteen or a female under the age of twelve.
Even when a non-Jewish child converts to Judaism or is converted by a parent, the child has the option at the point of bar or bat mitzvah age whether to sincerely accept his/her Judaism or to officially reject it. While we do not hear often of anyone rejecting Judaism at this point, it is still theoretically possible to do so.
When speaking of a Jewish child or adult, coming from a Jewish mother, it is Halakhically impossible for one to lose their ‘Jewish status.’ We have a concept in Judaism, “Even though [an Israelite, i.e. Jew] sins, he/she are still called Israel [Jew]. (Tractate Sanhedrin 44a, Baby. Talmud)
One who violates a major premise of Jewish belief or practice knowingly, is considered a sinner. Sins are transgressions requiring atonement in one fashion or another. Culpability is in accordance with a person’s immersion in the tenets of Judaism. Not everyone understands how serious a transgression it is to convert to another religion.
Some people may mistakenly believe that Christianity is a form of Judaism. There are religious movements that are dedicated to blurring the boundaries between Judaism and Christianity, even calling themselves: Jews for Jesus, Hebrew Christians, or Messianic Judaism.
Often the literature, garb, prayer books, church, take on the feel or appearance of ‘being Jewish.’ Some institutions call their pastors ‘rabbi’ and even recite ‘Shema’—‘Hear O’ Israel’ in Hebrew. One must be on their guard. Children, even more so than adults, are vulnerable to such efforts at proselytisation.
Many other faiths are seeking converts and adherents including but not limited to: Islam, Christian Science, Buddhism and Scientology.
In centuries past, Jews have been forced by means of impending death to convert to Christianity. While this is no longer the case, it is worthwhile briefly mentioning their status. Jews in Christian Spain under the persecutions after 1391 and the Inquisition (late 15th century) were forced to accept Christianity or die or be exiled. As we know, many were executed—thirty thousand men and women (according to Philip Birnbaum); many were exiled, however, numerous Jews known as Anussim (forced), Marranos (swine), crypto-Jews or Conversos accepted Christianity.
These Jews seemingly accepted Catholicism, while secretly holding fast to Judaism, at least secretly or in their hearts. Some were forced by the Church to eat pork publicly in order to demonstrate their fealty to Christianity. There is much written on this subject.
When the threat of death was later removed, many of these Jews wished to return to the faith of their ancestors and were required to reestablish themselves within the fold of Judaism. This was done by a semi-conversion to Judaism through the rite of circumcision, acceptance of the God of Israel, renunciation of any other belief and ritual immersion in a mikveh (ritualarium) before a beit din (rabbinic court).
Historically, one of the most sacred services in Judaism—‘Kol Nidrei—All Vows’ on the eve of Yom Kippur was instituted in order to allow all Jews, no matter how distant from their Judaism, including the Anussim to be allowed to participate in the service of the Day of Atonement leading to their readmission to the Jewish community and their faith.
While all of this leads us to understand some exaggerated pressure leading to a Christian conversion, a Jewish child in our day and age can hardly be placed into the same class. Normally, it may be a desire for conformity, to be like others or gain acceptance amongst friends.
Often one has no real concept of the richness of the Jewish Faith, assuming that others are richer than Judaism; not realizing or knowing that oftentimes other faiths have drawn from, and continue to draw from the wellsprings of Judaism.
Most likely, the Jewish child will not require anything more than a welcome back into the Jewish community, going to a Jewish school and synagogue services and possibly joining in with a Jewish youth group and activities.
As with all other serious Halakhic (Jewish legal) issues; a competent rabbinic authority should be consulted, to render an opinion while dealing with the specifics in this case.
Questions around conversion and Jewish identity present a number of complex issues and there are a variety of factors that can come into play in any given situation. In any case like this, I would urge you to consult with your rabbi. In the Conservative Movement, the rabbi of a synagogue sets the policies and practices for their particular community (mara d'atra).
As the question is presented, my presumption is that we are talking about a case of a Jewish woman who perhaps married someone who is Christian and the couple raised their child as a Christian. Let's say the child grows up and now, as an adult, rejects Christianity and wishes to reconnect with their Jewish roots. The question then is: how can this person, who was perhaps baptized and socialized in Christianity, now rejoin the Jewish people and practice the religion of Judaism?
According to Jewish law (halacha), a person born to a Jewish mother is Jewish, even if they do not practice Judaism. However, the question of someone who leaves Judaism to practice another religion poses some difficulties and raises doubts.
There is a principle that derives from the Talmud which states: "A Jew, even if he/she sins, is still considered a Jew." (see. BT Yevamot 47b, B'horot 30b, Sanhedrin 44a). The medieval commentator Rashi (11th C. France) interpreted this statement to mean that an apostate Jew who wishes to return should be treated with leniency and welcomed back without conversion. However, some scholars have noted that in Rashi's time, and for most of Jewish history, Jews who left the faith were most often coerced or pressured to convert. That is not the case today. Adults who leave Judaism and practice another religion do so by choice. These individuals should be treated as apostates and, according to the Conservative Movement, if they wish to return must undergo a formal affirmation of their Jewish identity through the ritual of immersion in the mikvah (t'vilah) and circumcision for males. (see J. Roth & A. Lubow, "Standard of Rabbinic Practice Regarding Determination of Jewish Identity" in The Proceedings of the Committee on Jewish Law and Standards, 80-85. p 178).
With the case of a child raised in another religion, an additional legal principle may be considered. The Talmud discusses the possibility that a child who was taken captive by gentiles and raised in another religion would not be liable for violations of Shabbat (BT Shabbat 67b-68b). From this idea, we might also take a lenient approach to a child raised as a Christian who wishes to be recognized as Jewish.
Based on our discussion thus far, it would be reasonable to conclude that the Torah ("d'oraita") does not strictly require conversion to Judaism in our case of a child raised in another religion. The only caveat would be that a male in this situation who was not circumcised would require brit milah, and if previously circumcised would require hatafat dam brit.
However, all this being said, as a practical matter Jewish rabbinic tradition ("d'rabbanan") dictates that we have to go beyond the narrow letter of the law and consider the very real emotional and social needs of the individual and community. A person who was raised as a Christian, perhaps baptized and educated in the church, and wishes to be recognized as Jewish has a need to be socialized into the Jewish community and learn how to practice the religion of their ancestors. This person should find a synagogue to which they want to belong and a rabbi to guide them in their integration into the community. It would be appropriate for them to undertake a course of study, like a conversion or "introduction to Judaism" class.
But, study and socialization are not quite enough. Ritual is how human beings mark moments of transition and meaning in life, imbuing them with holiness and intention. In order for this individual to be affirmed in their Jewish identity and in order for the community to be left with no doubts about this person's sincerity, a formal ritual is necessary. When the individual is ready, the rabbi should convene a beit din (rabbinic court) and bring this person to the mikvah for a ritual immersion (and if male, the person also needs brit milah or hatafat dam brit). Mikvah is a powerful ritual of rebirth. From the womb-like water of the mikvah the person who was raised as a Christian emerges renewed and affirmed in their Jewish identity. Only through such a ritual can this person be assured that their Jewish status will not be questioned.
You ask a great question, but we have to recognize that the answer is not a simple black and white response. First, we have to understand what it means to be Jewish. In order to claim Jewish identity, one must convert to Judaism, or be born of a Jewish mother (matrilineal descent). In my movement of Judaism, the Reform Movement, we proudly honor patrilineal descent as well – if the child has only a Jewish father – provided that they are raised affirming their Judaism through public acts of identification. So, Jewish identity is understood basically along these lines – a parental blood line – or conversion in.
When a Jewish person converts to another faith – as in the case of the child in question – we have two responses. First, the child – or anyone who converts “out” will always be considered Jewish – from a technical perspective. You can take the Jew out of Judaism, but you cannot take Judaism out of the Jew. So from a purely technical perspective, that person could claim to be of Jewish descent.
However - and this is the more pressing answer - that child would not be considered part of any normative Jewish community. Nor would any Jewish person feel comfortable referring to the child as a Jew – just because of some technicality. In this regard, we should consider one who has accepted another faith as an apostate.
I know people who grew up Jewish, and for various reasons have chosen to leave Judaism and identify as Christians. I make no comment or judgment on their faith journey – I just want them to be happy and righteous individuals. When someone asks them about their religion, they claim to be Christian. Perhaps they might also footnote that they grew up Jewish. That is fine. But when someone asks them their religion and they claim to be both Jewish and Christian – that is where they cross a line of understanding about religious identification. Judaism and Christianity are two powerful religious systems – but they are independent of the other. As Jews, we cannot intertwine Christian theology with our theology – because then it ceases to be Judaism. So we need to be careful in our language of religious identification. One can be Jewish, or one can be Christian, but not both - even with the technicality of Jewish blood lineage.
With regard to the child who converted out of Judaism, you also asked, “what must that child do to return to Judaism?” The quick answer I give is simply - nothing. When that child, or any adult, chooses to return to Judaism and identify solely as a Jew, there is no actual process to convert a technical Jew to Judaism. However, every community I know would still require some form of study and re-integration into Jewish life. I have worked with people who have been in these exact situations – they grew up Jewish, converted out, and decided to return. In their decision to re-commit to Judaism – they openly welcomed the opportunity to re-connect to their Judaism through study and understanding. At the end of that process, we do not have a “conversion,” rather; we call it something like an “affirmation” – using new language to describe that person’s decision to affirm their birthright.
I began my response by saying that the answer is not black and white. And so it goes with questions like these – that deal with real people, real emotions, and real journeys. There is an academic answer, and there is also a pastoral answer. The end result for the child in question is that they have chosen to convert to Christianity, and in doing so, they have left Judaism and Jewish life. However, on the technicality that they will always remain part of the blood line of the Jewish people – they have the opportunity, if they so choose, to re-claim their Jewish identity down the road without a formal conversion process back.
I hope this helps answer your question. Thank you for the opportunity to respond.