Q. A family where the parents became baley teshuva and strictly keep mitzvos and maintain a kosher home, but the children (aged 18 and 20) are not frum yet. Since they use the kitchen and cook for themselves, can the parents or invited guest eat there?
A. Poskim disagree whether one who does not observe Shabbos yet can effect food to became bishul akum. Piskey Teshuvo (Y.D. 112: 1) depends the above on the reason why our sages prohibited bishul akum (It may lead to intermarriage or to the ingestion of prohibited foods. See Yehuda Ya'aleh Y.D. 31, Tuv Ta'am Veda'as 2: 67). Tzitz Eliezer (8: 15) further relates permissibility to the kind of work done publicly on Shabbos and other conditions. Igrois Moshe (Y.D. 2: 46) deals leniently in regards to the milk of a mumar.
Horav Shlomo Miller Shlit'a opinion is that the parents have to be constantly aware of the foods the children bring to the house by supervising persistently the comestibles stored in the kitchen. However, in regards to bishul akum he also rules leniently.
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit'a