Judaism absolutely does not forbid any such thing.
My sister teachers at
Moriah College in Sydney which is a Jewish school, 40% non Jewish attend, including a large number of Japanese as the school itself has a superb educational reputation, coming in virtually every year with the highest marks in the high school certificate.
Not far down the road in Ocean Ave. Sydney, you will find the Temple Of Emanuel which is a very liberal Synagogue with all services in English.
Go to a service their and you will notice a healthy lot are not Jewish, but interested.. Also popular for Jews marrying non Jews, and in turn wanting to convert, more than likely to keep the parents happy, possibly the grandparents who may have been part of Hitlers regime..
I don't know much about religion, and no offence here, but from what I have seen and heard, many Islamic countries appear to be a human rights disaster, with the women taking the brunt..