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?
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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."