Is celebrating Christmas an innovation that leads to disbelief (kufr)? And does the necessity of accepting greetings and gifts and dealing with them result in the non-acceptance of future good deeds?

Celebrating birthdays is impermissible because it is an innovation (bid'ah) and involves imitating disbelievers. However, it is not an act of disbelief (kufr) and does not invalidate good deeds. One who receives congratulations or a gift should gently explain the religious ruling to those offering them. If they fear damaging the relationship, they may accept the gift, clarifying that it is for friendship and not for the celebration, and ask them not to repeat such an act.