We've discussed previously that halacha prohibits the burial of non-Jews in the same cemetery as Jews. But what about born-Jews who converted out? What about Jews who were simply atheists?
YU Torah online has an extensive document on death and mourning.
In Section 12, 36 קבורת משומד it quotes
a. Iggros Moshe – he deals with a woman who converted to Christian Science. The question is if she can be buried in a Jewish cemetery.
i. We can’t say that she was “crazy” because even though all forms of Avodah Zarah are crazy they are still chayav.
ii. We can’t even say that she was chozer b’teshuvah by going to a doctor [a violation of the (Christian Science) faith] because she might have been forced by her pain. We must maintain the chazaka that she is a mumar.
iii. She should be cleaned before burial like a normal Jew, but shouldn’t be buried in the Jewish cemetery.
iv. Yet, since the grave is itself a kapara, she can be reburied in a Jewish cemetery after 12 months.
- [Due to the fact that in this particular case there was a minimal doubt that she was chozer b’teshuvah because she ripped her burial plot certificate, Rav Moshe allowed her to be reburied in a Jewish cemetery immediately. She didn’t have to wait 12 months.]
which is a source for the question of conversion.
Regarding the atheist, I refer you to my (downvoted) answer to Should someone who isn't 100% certain of God's existence be considered a kofer? where I quote an article that quotes the sixth Lubavitcher Rebbe, Rabbi Yosef Yitzchak Schneersohn (1880-1950) who told one self-proclaimed atheist, "We are all believers in G-d. It is just a matter of definition."