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
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."