Q. Someone I know who converted to Christianity insisted on saying Kaddish at his mother’s funeral. Should the rabbi have stopped him?
The consensus was that such a person was residually Jewish, not entitled to Jewish privileges like being called to the Torah but not exempt from obligations like clearing the chametz from his house before Pesach. This applied even if the former Jew no longer counted himself as Jewish.
The rabbis quoted a passage from the Talmud, “Though a Jew has sinned he is still a Jew” (Sanh. 44a); on the verse in Joshua (7:11), “Israel has sinned”, the sages said that even though Israel sins he is still called Israel. A convert to another faith is legally or technically not deemed to be a non-Jew except that he is not entitled to the privileges of being Jewish, as stated above.
The convert you mention could have excused himself from saying Kaddish, but since Kaddish is an obligation the rabbi was right not to stop him saying it, especially since it is universal in theme and language.
There is however the symbolism of Kaddish, generally understood as a commitment to honour a parent’s memory by being a faithful Jew, and whether this applies when to a person who has officially turned his back on Judaism is a question.