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 to join in the non-Muslim festivals because this entails imitating or resembling them and taking part in their festivals is a kind of befriending them and showing love for them.

Initiating a greeting to a non-Muslim is prohibited. But if they greet us, we have to respond to them. However, it is permissible to greet a non-Muslim first if that serves a purpose, or for fear of his harm, or because of blood ties, or for a reason that requires that.