A rare case when Christians are celebrating Christmas [25th December claimed to be the birthday of prophet Jesus (PBUH)] and Muslims are celebrating Eid-e-Milaad-un-Nabi [12th Rabi-al-Awwal claimed to be the birthday of prophet Muhammad (PBUH)] on the same day - Gregorian calendar meets Lunar calendar. Turns out, none of these celebrations have any real basis in the history of their respective religions - sorry to hurt you if I have done so by saying this.
There is no evidence to support that Jesus (PBUH) was born on this day in the Gregorian calendar. It was a traditional pagan celebration in the pagan culture which was later manipulated by the humans to be called the birthday of Jesus (PBUH). But their is no proof to claim that this was the day which he was born in. What is it that everyone is celebrating? Who is Santa? What is Christmas? What are the jingle bells? Do they really have anything to do with Jesus being born (PBUH)? Or are these simply some happy smiley stuff to have and to cherish in the homes during this date with no original basis to the religion even though everyone claims the date to be associated with the religion?
There is no evidence to support that Muhammad (PBUH) was born on this day in the lunar calendar. Muhammad (PBUH) himself never did any special act for this date (or even for the occasion of his birthday). He never instructed his immediate followers to do that. His immediate followers never did that after his passing for several generations. There has been absolutely no religious association with the matter in any way. Many years later, some Muslims thought of making an occasion out of it and started associating religious piety and religious holiness to it; whereas none of this ever existed during the presence of Muhammad (PBUH). Why? Did these Muslims suddenly receive newer modern revelations that this is a holi day that they started associating innovated holiness to it? Is there really any holiness for this date over the other dates, or is it just that Muslims are also swaying away with a desire for "we also want to have our prophet's birthday like they do".
Whether we celebrate birthdays or not is a different topic in & of itself. But today, the foundation of the basis of these celebrations are not even correct. What are people celebrating actually? Just going along with the norms of the people and the societies around them? Being happy with family & friends for a day which is not even a real day? Or is there really some basis to it? Shouldn't we be mindful of what we are celebrating? Or should we rather simply go with the flow just because everyone else is doing it? People still wanna be happy-go-lucky about these occasions even if there is no truth in it. How deluded are we then?
P.s. Muslims recognize both Jesus and Muhammad as the Prophets of their religion (Peace Be Upon Them Both).