It is not permissible for the Muslims to exchange greetings on the occasion of the Gregorian New Year, and it is not permissible for them to celebrate it

What is forbidden with regard to congratulating the Christians on the occasion of their festivals is expressing joy to them, being overly polite and showing approval of their actions, even if that is only expressed outwardly without feeling it inwardly.

There is nothing wrong with accepting a gift from a non-Muslim on Christmas and that is not regarded as participating in it or approving of it, rather it should be accepted as an act of kindness with the aim of softening his heart and calling him to Islam.

It is not permissible for the Muslims to attend the festivals of the polytheists, according to the consensus of the scholars. It is also prohibited to greet the non-Muslims on Christmas and other religious holidays.

A Muslim man can marry a Chrisitan or a Jewish woman. But if the woman who wants to marry a Muslim man is not one of the people of the Book, then it is not permissible for a Muslim to marry her.