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Does halacha allow letting a Jewish baby nurse from a non-Jewish woman (assuming Jewish wet nurses are available)?

The Gemara says that Baby Moses refused to nurse from a non-Jewish woman, saying, "Shall a mouth that will speak with the Divine Presence nurse impure milk?" [Sotah 12b] Does this teaching apply only to those destined to speak to God face-to-face, or to everyone?

(This is not really a chalav Yisrael issue. But on the other hand, the Ramban says, "You are what you eat.")

The Chayei Adam in 66:14 writes a two sentence Halacha:

According to the letter of the letter of the law, one is allowed to have a non-Jew nurse a Jewish child, but if possible, one should avoid allowing a non-Jew nurse a Jewish child since it 'taints the heart'.

Similarly, a Jewish woman who needs to eat forbidden foods for health purposes should hire another [Jewish] woman [to nurse the child during that time].

מדינא מותר לתינוק ישראל להניק מנכרית מ״מ אם אפש ר ע״י ישראלית לא יניחו
להניקו מנכרית דמטמטם הלב ומוליד מזג רע וכן מינקת ישראל שצריכה לאכול
מאכלי איסור לרפואה ל א יניחנה לינק אלא ישכיר אחרת

Interestingly, the first sentence is not found in most editions of the Chayei Adam (the quote above can be found in this edition). Most editions of the Chayei Adam just have the second sentence (that a Jewish woman who has to eat non-Kosher should not nurse her child). It has been speculated that the first half of the Siman was removed in later editions in order to placate the censors.