Assuming that one can ascertain that food cooked by an irreligious Jew is kosher, is the food still prohibited due to Bishul Akum? Does this also apply in a case of need, such as one visiting an irreligious relative, where it may be embarrassing and inconvenient to procure other food?
Halachically Speaking (7:2) has a great overview of this question:
There is a discussion in the poskim regarding the status of a Jew who is not observant. The Rambam states that a Jew who is mechalel Shabbos (openly) is considered like a non-Jew for all mitzvos. The Pischei Teshuva debates the status of a mechalel Shabbos (mumar) in regard to bishul akum, since the prohibition is dependent on the two reasons for the issur of bishul akum:
- because we are concerned that the Jew will come to marry the non-Jew; it is questionable if this applies to an irreligious Jew
- a concern that the nonJew will mix some non-kosher ingredients into the food, which would apply to an irreligious Jew
Some poskim rule that food cooked by a Jew who is not observant is forbidden, while others permit it. Other poskim say that nowadays it is difficult to find someone who is a true mumar, as most assimilated Jews are tinokos shenishba and transgress the Torah accidentally.
Contemporary Opinion: The opinion of Harav Yisroel Belsky Shlita is that the custom is to permit the cooking of a non-religious Jew. This opinion is based on a ruling from Harav Moshe Feinstein zt”l that the main reason for the prohibition of bishul akum is intermarriage, and we are not concerned about intermarriage regarding non-frum Jews.
Nonetheless, it is preferable to be stringent l’chatchilah even by a tinok shenishba, but b’dieved it is permitted. This is the custom among the kashrus agencies.
From http://www.shemayisrael.com/parsha/halacha/Volume_7_Issue_2.pdf, which also has all the references in footnotes
Rabbi Elyashiv Zatzal in Kovaitz Teshuvos 3:115 says that it is possible that the Gezaira of Chasnus applies also to a Mechalel Shabbos. Even though technically one can marry a non observant Jew, the Gezaira was made to keep us separate.
יש מקום לומר, שכאשר גזרו על דבר משום חתנות,גזרו גם על מחלל שבתות. ואף על פי שאין איסור ממש להתחתן איתם, אבל הגזרות האלה נגזרו במטרה להרחיק ולהבדיל
Maharam Schick Orach Chaim 281 also says that anywhere the Chachomim made a Gezeira on non-Jews it applies to Jews that are Mumrim.