It’s a Machlokes Haposkim whether such a person’s food is Bishul Akkum. Most people seem to assume that it’s Assur but someone (I think the Pishchei Tshuvah) on the page of the Shulchan Aruch is the only source I have actually seen on this issue and he says it’s Muttar. Because the Issur is only a Gezeirah so that you don’t marry the Goy’s daughter, and a Mumar’s daughter is Muttar to marry, so it’s okay.
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