Traditional Jewish thought always assumed the Messiah would come, then the Jews would return to Israel and self-government. When, in the 19th century, Jews began contemplating returning on their own, in the absence of a Messiah, traditional Jews were unsure about whether that, too, could be a fulfillment of the divine promises of redemption. It didn't help, unfortunately, that many of the Jews who were in the vanguard of this great movement were not observant (and some were anti-observant). The State that came about in 1948 was certainly sensitive to religion in many ways, but was not a religious state, which many Jews assume the Messiah will eventually bring (and which I imagined in my book, Murderer in the Mikdash).
For all of these reasons, there are Jews who do not see the establishment of the State as a cause for celebration. We can hope and pray for a time when not only you and me recognize the wonders of the State, but that it become a State that all Jews, worldwide, can celebrate with a full heart.
Just as I would not think it appropriate to ask an Ultra-Orthodox Jew why Conservative Jews do or do not do something, I am hesitant to respond to this question. My simple understanding is that the Ultra-Orthodox are awaiting the coming of the Messiah to accept a Jewish polity in the Holy Land. For a more complete and nuanced response I suggest that the question be addressed directly to one who rejects the celebration of Yom Haatzmaut.
I begin with a disclaimer: the following response is a generalization and, as with every group, there are those who do not fit the generalization. That being said, many Ultra-Orthodox Jews (Haredim) believe that the modern State of Israel was established prematurely without God's blessing. Because of this, while many live in Israel, they abstain as much as possible from matters of the state. For this group of Jews, Israel can only come into existence when the Messiah has come and the Temple in Jerusalem is rebuilt.
In 2009 Eliezer Hayon of www.ynetnew.com wrote a controversial article with the headline, “Why Haredim Don’t Honor Memorial Day.” He wrote, “Ultra-Orthodox don’t participate in national Memorial, Independence Day [Yom Ha’atzmaut] not out of spite, but because these days mean nothing to them.” Hayon writes, “Memorial Day and Independence Day are not part of their historical chronology.” He adds, “The haredi street does not celebrate Independence Day not because haredim think – like the eccentric minority that calls itself Neturei Karta – that this is a sad day, but because Independence Day, which for many is a national day and a highly important historical date, is for them a day like any other.”
In the United States the celebration of Israel Independence Day is often a time when Jewish organizations and synagogues of different denominations, from liberal Jews to the Modern-Orthodox, cooperate in forming a common celebration. It is a way to express solidarity with the state of Israel; and, like in Israel, the Ultra-Orthodox often self select not to participate and view the day as any other.