The Gemara (BM 87b) relates that at the time that Avraham made a feast for Yitzchak'a birth, the nations mocked him and Sarah, saying that they adopted him, or that he was Avimelech's son with Sarah. HaShem made Yitzchak look just like Avraham so everyone could see he was the father, and Sarah nursed all of their guest's children to show that she was physically capable of being his mother.
In those times, everyone worshipped idolatry except for Avraham and his family and followers. After all, Avraham was called the Ivri because he was on one side and the world was on the other (Pesikta Rabasi 33:1). So how was Sarah able to do this, when the Mishnah (AZ 26a) says that one may not nurse an idolatress's baby? Avraham and Sarah observed the Torah before it was given (see, for instance, BM ibid., Bereishis Rabbah 84:4, et. al.). Granted that the Gemara there discusses that one may do so in cases of Eivah, what Eivah would there be in our case if she refused? The heter is Eivah, not Leitzanus.