In spirit, most Muslims have no problem with the concept of celebrating the birth of Jesus (as). There are some Muslims who avoid celebrating birthdays altogether. But Shia Muslims as a matter of course find it meritorious to honor and remember the saints and prophets of God on the birthdays, death days and other significant dates.
We now know that December 25 is a wrong date for the birth of Jesus (as) and was chosen to coincide with certain pagan activities to ease their conversions from paganism but allowing them to incorporate some pagan traditions. I guess the more favored date now is sometime in April, around 4 or 5 B.C.
Muslims believe in Jesus (as), and in that sense we are Christians.
1. We believe Jesus (as) was born of the Virgin Mary by a miracle from God.
2. We believe Jesus (as) spoke to people while still a newborn.
3. We believe Jesus (as) performed numerous other miracles through the power of God including having the ability to raise the dead.
4. We believe Jesus (as) was a prophet of God who delivered the message (gospel) about how to get saved from hell and that he was supported by Ruh al Quddus, sometimes called the Holy Spirit. The gospel was a scripture revealed to Jesus (as) to deliver to mankind.
5. We believe Jesus (as) never committed a sin ( and actually we believe this of all prophets).
6. We believe Jesus (as) is not part of a triune God - we believe in a Unitarian God.
7. We believe Jesus (as) is not God in the flesh but is a holy man who prayed to God and carried out God's will on earth.
8. We believe Jesus (as) was not crucified on the cross but was raised to heaven by God.
9. We believe Jesus (as) will return at the time of Armageddon to help establish God's rule on Earth.
10. There is no Joseph as a father of Jesus (as) or husband of Mary mentioned in the Muslim Scriptures.
11. John the Baptist is also mentioned in the Qur'an as a prophet of God just preceding Jesus (as) and a supporter and preparer for Jesus (as).
Some pertinent passages from the Qur'an for Christmas about Jesus and Mary:
So her Lord accepted her with good acceptance and made her grow up a good growing and gave her into the charge of Zakariya; whenever Zakariya entered the sanctuary to see her, he found her with food. He said: O Mary! where did you get this? She said: It is from God. Surely God gives to whom He pleases without measure. (3:36)
And the angels said: O Mary! Surely God has chosen you and chosen you above the women of the world. (3:41)
She (Mary) said: My Lord! Shall there be a son born to me while no man has touched me? He said: Even so, God creates what He pleases; when He has decreed a matter, He only says to it, Be! - and then it is. (3:46)
And most certainly we gave Moses the Torah and We sent apostles after him one after another; and We gave Jesus son of Mary clear arguments and strengthened him with the Ruh al Quddus. (2:87)
Say: We believe in God and what has been revealed to us, and what was revealed to Abraham and Ishmael and Isaac and Jacob and the tribes, and what was given to Moses and Jesus and to the prophets from their Lord; we do not make any distinction between any of them, and to Him do we submit (are Muslims). (3:83)
And We made a covenant with the prophets and with you, and with Noah and Abraham and Moses and Jesus son of Mary, and We made with them a strong covenant. (33:7)
And We sent after them in their footsteps Jesus, son of Mary, verifying what was before him of the Torah and We gave him the Gospel in which was guidance and light, and verifying what was before it of the Torah and a guidance and an admonition for those who guard against evil. (5:46)
And mention Mary in the Book when she drew aside from her family to an eastern place; So she took a veil to screen herself from them; then We sent to her Our spirit, and there appeared to her a well-made man. She said: Surely I seek refuge from you with the Beneficient God, if you are one guarding against evil. He said: I am only a messenger of your Lord that you will give birth to a pure boy. She said: How shall I have a boy when no mortal has touched me nor have I been unchaste? He said: Even so, your Lord says: It is easy to Me, and that We may make him a sign to men and a mercy from us; and it is a matter which has been decreed. So she conceived him, then withdrew herself with him to a remote place. And the throes of child birth compelled her to betake herself to the trunk of a palm tree. She said: Oh, would that I had died before this, and had been a thing quite forgotten. Then the child called out to her from beneath her, 'Grieve not, surely your Lord has made a stream to flow beneath you, and shake toward you the trunk of the palm tree and it will provide you with fresh ripe dates. So eat and drink and refresh the eye. Then if you see any mortal say "Surely I have vowed a fast to the Beneficient God, so I shall not speak to any man today. And she came to her people with him (Jesus), carry him. They said: O Mary! Surely you have done a strange thing. Your father was not a bad man, nor was your mother an unchaste woman. But Mary pointed to the baby. They said: how should we speak to a child in the cradle? But Jesus spoke, and said: Surely I am a servant of God; He has given me the Book and made me a prophet. And He has made me blessed wherever I may be, and He has enjoined on me prayer and poor-rate so long as I live. And He has made me dutiful to my mother, and He has not made me insolent or unblessed. Peace on me the day I was born, and on the day I die, and on the day I am raised to life again.' Such is Jesus, the son of Mary; this is the saying of truth about which they dispute. It beseems not God that He should take to Himself a son; glory be to Him; when He decrees a matter He only says to it "Be" and it is. (19:16-36)
And when you (Jesus) determined out of clay a think like the form of a bird and by My permission then you breathed into it and it became a living bird, and you healed the blind and leprous by My permission; and when you brought forth the dead by My permission. (5:110)
When the disciples said: O Jesus Son of Mary, will you Lord consent to send down to us food from heaven? He said: Be careful of your duty to God if you are believers. They said: We desire to eat of it and that our hearts should be at rest, and that we may know that you have indeed spoken the truth to us and that we may be the witnesses of it. Jesus Son of mary said: O God our Lord, send down ot us food from heaven which should be to us an everrecurring happiness, to the first of us and to the last of us, as a sign from Thee, and grant us means of subsistence, and Thou art the best of Providers. God said: Surely I will send it down to you, but whoever shall disbeliever afterwards from among you, surely I will chastise him with a chastisement with which I will not chastise any one from among the nations. (5:112-115)
And the Messiah (Jesus) said: O Children of Israel! Serve God, my Lord and your Lord. Surely whoever associates others with God, then God has forbidden to him the paradise, and his abode is the fire, and there shall be no helpers for the unjust. (5:72)
And Jesus Son of Mary said: O Children of Israel! Surely I am the apostle of Allah sent to you, verifying that which is sent before of the Torah and giving the good news of an apostle who will come after me, his name being Ahmad (Comforter). (61:6)
Surely the likeness of Jesus is with God the same as the likeness of Adam; He created him from dust, then said to him, Be, and he was. (3:58)
And they say: God has taken to Himself a son. Glory be to Him; rather whatever is in the heavens and the earth is His; all are obedient to Him. (2:116)
And they say: The Beneficient God has taken to Himself a son, Glory be to Him, Nay! they (all prophets including Jesus) are honored servants, they do not precede Him in speech and only according to His commandment do they act. (21:26-27)
Certainly they disbelieve who say: Surely God is the third of three; rather there is no god but the one God. (5:73)
The Messiah, Son of Mary is but an apostle; apostles before him have indeed passed away; and his mother was a truthful woman; they both used to eat food (they were humans, not gods). (5:75)
And their saying: Surely we have killed the Messiah, Jesus son of Mary, the apostle of God; and they did not kill him nor did they crucify him, but it appeared to them so (like Jesus) and most surely those who differ therein are only in a doubt about it; they have no knowledge respecting it, but only follow a conjecture, and they killed him not for sure. Nay! God took him up to Himself; and God is Mighty, Wise. (4:157-158)
And God said: O Jesus I am going to terminate the period of your stay on earth and cause you to ascend unto Me and purify you of those who disbelieve and make those you follow you above those who disbelieve to the day of resurrection; then to Me shall be your return. (3:54)
And when God will say: O Jesus Son of Mary! Did you say to men, 'Take me and my mother for gods besides God' he will say: Glory be to thee, it did not befit me that I should say what I had no right to say; if I had said it, Thou wouldst have indeed known it; Thou knowest what is in my mind and I do not know what is in Thy mind; surely Thou art the Great Knower of unseen things. I do not say to them aught except save what Thou did enjoin me with; I said to serve God, My Lord and your Lord, and I was witness of them so long as I was among them, but when Thou caused me to leave, then Thou were the watcher over them. (5:116-117)