According to a facebook post by renowned Islamic scholar, Doctor Zakir Naik said, No Muslim is a Muslim if he does not believe in Jesus Christ.
He also quote verse from the holy quran which says “O People of the Book (Jews and Christians)! Commit no excesses in your religion: Nor say of Allah aught but the truth. Christ Jesus the son of Mary was (no more than) a Messenger of Allah, and His Word, which He bestowed on Mary, and a spirit proceeding from Him: so believe in Allah and His Messengers. Say not ‘Trinity’: desist: it will be better for you: for Allah is but one God: Glory be to Him: (far exalted is He) above having a son. To Him belong all things in the heavens and on earth. And enough is Allah as a Disposer of affairs.
Al Qur’an 4:171
However, Only God knows who is worshiping him. Christmas is a season of love and sharing among human beings. It may not be the day Christ was born but is a day that unites people all over the world in love and sharing. For the sake of the unity and love that it brings, is it not enough to call for best wishes from all humans to humans.