Watch this lecture by Sheikh `Abdur-Rahim Green about the unity of message brought by Moses, Jesus, and Muhammad (peace be upon them all).
Each Abrahamic religion has a prophesied person to emerge towards the end of the world as a portent of the Last Day, be he the Antichrist or Jesus Christ
Muslims do not bother themselves a lot with Christmas itself as a baseless observance. They rather object to many Christian beliefs based on this occasion
The Nativity accounts in the New Testament are illogical, whereas their counterparts in the Quran are quite logical.