Courtesy of a commenter who didn't know what the problem is, I posted this response then realized it warranted being another post.
The PROBLEM is that there are not 2,000 but, over 300,000 "Almost Jews" in Israel who are not halachically Jewish and don't want to be. These are primarily patrilineage Jews from the former Soviet Union. However, there are patrilineage Jews from other countries, as well as converts with conversions good enough for the Law Of Return, yet not good enough for marry and bury in Israel.
These "Almost Jews" live, breathe, think and celebrate their Jewish year the same way that other secular Jews do. They don't keep kosher and Shabbos. However, they have a seder for Pesach. They celebrate Chanukah and high holidays. This is what plenty of secular Jews do. They are indisguishable from a halachically Jewish secular Jew. However, they are not Jewish due to a technicality.
This is a problem because there is now assimilation taking place in the Jewish state between these masses of "Almost Jews" and Jews. This is why they have overturned so many conversions from Rabbi Chaim Druckman. Originally, the solution was to convert them but since they don't want to be observant, they just sort of handed over the conversions after a they learned a little more than they previously knew.
Currently, non religious marriage and burial is not available to these people. What are these people to do? They aren't Xtians. They aren't muslims. They do not wish to marry and bury under either of these auspices. I guess you can say they are noahides, however, they grew up thinking they were Jewish and so, they are more Jewish than a regular noahide. However, the matter still remains, they are not Jewish.