Is it permissible to accept a gift from a Muslim father who is not religiously committed, on the occasion of his son's birthday, with the intention of drawing closer to him and later alerting him to the impermissibility of this act?

Celebrating Christmas is an innovation and an imitation of the disbelievers, so it is not permissible for Muslims to imitate them in it. A gift is permissible in its origin, but offering or accepting it for the sake of celebrating Christmas is not permissible, due to the prohibition against this act.