Answering Amen
Maran Ha’Shulchan Aruch (Ch. 215, Sec. 2) rules: “If one hears a fellow Jew recite any blessing, one must answer Amen, even if one has not heard him recite the entire blessing from beginning to end. However, if the one reciting a blessing is a heretic or non-Jew, one should not answer Amen. The Rama adds, however, that if one heard the non-Jew recite the entire blessing, including the words “Hashem, Elokeinu Melech Ha’Olam,” one should, in fact, answer Amen.
The Reason
The reason why one cannot answer Amen to the blessing of a non-Jew is because we are concerned that he recited the blessing to foreign deities and idolatry, such as devout Christians who recite grace to their god before eating. This explanation is quoted by the Rosh (Berachot 8:5) and other Rishonim.
Based on this, if one hears a non-Jew recite the entire blessing, one should answer Amen, for we can be certain he did not mention the name of another deity.
On the other hand, the Rambam (Ch. 1 of Hilchot Berachot, Halacha 13) rules that one may never answer Amen to the blessing of a non-Jew, even if one heard the entire blessing, for we are concerned that he is thinking about his deity in his heart. This is echoed by many other Rishonim and seems to be the opinion of the Shulchan Aruch as well (see Halichot Olam, Vol. 3, p. 122). However, as we explained above, the Rama rules in accordance with the Rosh that as long as one hears the entire blessing recited by a non-Jew, one should answer Amen.
The Bottom Line
Halachically speaking, according to the Sephardic custom, one should never answer Amen to a blessing recited by a non-Jew, however, Ashkenazim may, if they hear an entire blessing being recited by a non-Jew.
The Law Regarding Muslims
Nevertheless, the Yalkut Yosef (Berachot, Ch. 215, p. 376) rules in the name of Rabbeinu Yaakov Castro that the law is different regarding Muslims. Since we know that they believe in one God and they do not appendage any other deities to Him, although they may believe in many other foreign theologies foreign to Judaism, we may accept the blessings they recite in our language as a satisfactory blessing, and one may answer Amen to their blessings.
Summary: According to the Sephardic custom, one may not answer Amen to blessings recited by non-Jews, with the exception of blessings recited by Muslims when one hears the entire blessing. According to the Ashkenazi custom, however, one may answer Amen to a blessing recited by any non-Jew as long as one hears the entire blessing being recited.
