All Non-Jews
Does not serve avoda zara. The gezeira against bishul akum applies to all non-Jews, even those who do not serve avoda zara, as the issur of intermarriage applies to all of them. Thus, even if food was cooked by a Muslim who does not serve avoda zara, it may not be eaten (שו''ת הר''ן סי' ה', ב''י סי' קכ''ג בשם הרשב''א, שו''ת רמ''א סי' קכ''ד, פמ''ג סי' קי''ב שפ''ד סק''ב, חת''ס פתיחה להל' יי''נ ).
Childless. Chazal made their gezeira even for non-Jews with whom intermarriage is not possible, e.g., a non-Jew who is childless or sterile. Chazal did not make distinctions in the matter and forbade food cooked by any non-Jew (שו''ת הרשב''א ח''א סי' רמ''ח, דרכ''מ סי' קי''ב, ט''ז שם סק''א, ש''ך סק''ד ).
Jew present overseeing. Even if a Jew is in the presence of the non-Jewish cook or is supervising him to make sure he does not mix in any assur foods, the food is still assur due to bishul akum, as the gezeira is to prevent intermarriage. Unless the Jew does something in the cooking that is effective to permit it, as will be explained in the coming issues בעזהשי"ת , the food is assur (שו''ת ריב''ש סי' תקי''ד ).
Food Cooked by a “Mumar”
There is a machlokes haposkim whether or not food cooked by a true Jewish mumar [intentional sinner] who is treated like a non-Jew (ע''פ שו''ע יו''ד סי' ב' וסי' קי''ט ) is subject to the issur of bishul akum. This is very relevant when public mechallelei Shabbos are employed in food establishments.
Concern for assur foods. According to the reason for the gezeira out of concern for assur food, food cooked by a Jewish mumar would also be assur, as the reason applies to him too (תפארת למשה הובא בפתח''ת ריש סי' קי''ג ).
Intermarriage. However, according to the majority of Rishonim, that the gezeira of bishul akum is to prevent intermarriage, one can be meikel with a Jewish mumar, as even though he is a sinner, he is still a Jew (ר''י מקורביל סמ''ק סי' רי''ט אות רל''א, שו''ת מהר''י אשכנזי יו''ד סי' ט''ז, כף החיים סק''א, שו''ת אג''מ יו''ד ח''א סי' מ''ה).
Machmirim. Nevertheless, many poskim are machmir. Since a mumar has the status of a non-Jew, the general gezeira to prevent intermarriage applies to him too so as not to make distinctions, and one may not eat food he cooks (משמעות רש''י חולין דף מ''א ע''ב ד''ה בדיקה, רמב''ן ור''ן חולין דף ד' ע''ב, פמ''ג או''ח סי' שכ''ה א''א סקכ''ב ויו''ד סי' קי''ב שפ''ד סק''ב, שו''ת מהר''ם שיק או''ח סי' רפ''א ד''ה אמנם, שו''ת מנחת יצחק ח''ג סי' ע''ג, מרן פוסק הדור בתשוה"נ ח''ו סי' צ').
In practice. Since there is a machlokes haposkim about his status, l’chatchila one should satisfy the machmirim and adhere to the halachos of bishul akum even for a Jewish mumar. B’dieved though, or in a pressing situation, there is room to be meikel. Some factor in the meikel opinions when there is an additional reason to allow the food to be eaten (בין ישראל לעמים פ''ה ס''ו ). The more basic kashrus agencies are usually meikel in this; the higher-level ones are machmir l’chatchila.
