How do we respond to those who permit celebrating Christmas on the grounds that it is a custom and not an act of worship, and thus not considered an innovation (bid'ah)?

Celebrating birthdays is an alien custom to Muslims, and it is an imitation of the enemies of Allah and an assimilation to them, and we have been forbidden from imitating them. Birthdays were not part of the guidance of the Prophet, peace and blessings be upon him, nor his companions. Anything innovated in religion that is not part of it is rejected. Moreover, participating in the overt customs of disbelievers leads to similarity and agreement in character, and removes the distinction between Muslims and others.