Is it OK for a Jewish to marry a Muslim?
From the Jewish perspective, is it OK for a Jewish woman to marry a Muslim man?
Depends on your interpretation of Jewish law. There are intermarriages in the Torah, for example, David and Elijah both marry foreign wives. Deuteronomy implies that intermarriage to Edomites or Egyptians was acceptable “Thou shalt not abhor an Edomite, for he is thy brother; thou shalt not abhor an Egyptian, because thou wast a stranger in his land.” לֹא-תְתַעֵב אֲדֹמִי, כִּי אָחִיךָ הוּא; לֹא-תְתַעֵב מִצְרִי, כִּי-גֵר הָיִיתָ בְאַרְצוֹ. Israelites were generally accepting of new members of the tribe, though this usually meant a gentile converting.
This changed after Babylonian Exile as Jews began to fear the survival of their community, and many Prophets in Nevi’im advised against intermarriage. Ezra explicitly forbid intermarriage between a Jew and any non-Jew. Keeping this in mind, children between a Jew and a non-Jew are not considered illegitimate (like the children of an incestuous relationship).
In summary: Most rabbinical authorities would say intermarriage is forbidden, though I find that in the Jewish community intermarriage between Jews and Muslims is tolerated much more than intermarriage to Christians.
Hope that helps
It is matter of debate in traditional Orthodox Judaism, whether the Torah prohibits only marriage with the 7 ancient polytheistic Canaanite tribes, who are not around anymore, or with any idol worshipers. Many well known codifiers of the Jewish law hold the opinion that marriage with non-Jews who do not worship idols is not forbidden directly by the Torah, but there is a Talmudic/rabbinical prohibition against it intended to prevent assimilation of the Jews.
A group of well-known rabbis in 19th century France proclaimed that civil marriage between Jews and Christian or Muslims is not forbidden, because without a religious marriage it’s more like a pilegesh relationship (somewhat similar to mutah in Shia Islam), but this is a controversial topic in itself and I doubt that you’ll find many rabbis who would support this marginal theory.