Ruling 2416: And a Muslim man cannot marry women who are disbelievers other than those from among the People of the Book. However, there is no problem if a Muslim man contracts a temporary marriage with Jewish or Christian women but, based on obligatory precaution, he must not contract a permanent marriage with them. As for Zoroastrian women, based on obligatory precaution, a Muslim man must not contract marriage with them, not even a temporary marriage.
A man who has a Muslim wife cannot contract marriage with women who are from among the People of the Book without the permission of his wife; rather, even with her permission, it is not permitted (jāʾiz) for him to marry them.