An irrelegious Jew does NOT create Bishul Akum, because the Gezeira was to prevent intermarriage and there is no prohibition against marrying the daughter of a sinner. Sources: Tiferes l’Moshe, Pischei Teshuva, Yabia Omer, Halichos Olam, Tzitz Eliezer. There are grounds to be stringent based on the Pri Chadash, but even he only considers it a Chumra.
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