There are two primary reasons that tattoos are not accepted in the Jewish community.
The overall Reform position on this seems to be in line with much of what is said in other matters: Jewish tradition is not in favor of this act, and we discourage it, but each person may act with autonomy and make their own decision about it.
As for the concern you express about future burial, I am sorry to shoot down a myth upon which many Jewish parents have relied for years, but I don’t wish to perpetuate a falsehood. Having a tattoo is not in and of itself enough to prevent someone who is Jewish from having a Jewish funeral or being buried in a Jewish cemetery. For example, I cannot imagine any Jewish cemetery that would refuse burial for a Holocaust survivor simply because they had a tattoo.
Restrictions on burial in a cemetery tend to be set by the rules of the cemetery in question. A cemetery run by an Orthodox group may have different rules than one run by a Reform group, and both may differ from a cemetery run by a Conservative group, but equally true is that two Reform cemeteries may have very different rules. There is no overall rule that one can refer to as the definitive statement.
As a general matter, I would suggest that the family of a Jewish person who is to be buried will be able to find a Jewish cemetery where that person can be buried. They may find that one or another cemetery will not agree, but in the end, a Jewish person is likely to be accepted for burial in a Jewish cemetery. The existence of a tattoo (or several) may affect which cemetery, but should not prevent a Jewish funeral and burial.