I was at a talmud chacham’s shabbos table with an irreligious Jew. When the time came to bentch, the Talmud Chacham skipped the Zimun and just started bentching. Is there a halacha about not making a zimun with a non religious Jew?
The Mishnah Berurah (199:2) writes that a person who does not observe basic halachos cannot be joined for a zimun. For a non-religious Jew, Rav Shlomo Zalman Auerbach ruled that if he is categorized as a tinok she-nishba (he grew up in an irreligious environment and was never ‘given a chance’) can join for a zimun, though he should not be the one to lead the zimun (cited in Vezos Ha-Berachah).