Here are three popular religious holidays that Muslims do NOT celebrate. They are:
Anas ibn Malik reported: The Messenger of Allah, peace, and blessings be upon him, arrived in Medina during two days in which they were celebrating. The Prophet said, "What are these two days?" They said, "We would celebrate these two days in the time of ignorance." The Prophet said, "Verily, Allah has replaced these two days with two better days: the day of sacrifices and the day of breaking fast" (Sunan Abu Dawud 1134).
This is one explanation for why Muslims do not celebrate Halloween.
Another reason is that the holiday and its traditions are either based on ancient pagan culture or Christianity. Since none of these honor Islamic faith or beliefs, everything about Halloween can be considered as idolatry (shirk).
In the words of Dr. Muzamil Siddiqi, former president of the Islamic Society of North America (ISNA): "Halloween is an old pagan holiday of the witches and the dead. Later some Christians tried to Christianize it by calling it "All Saints Day." However, there are still many Christians who resent it and consider it a bad holiday. Some of them even call it a "holiday." Whether Christians accept it or not, we Muslims should not accept this holiday. Muslims should not participate in this holiday."
Islam is not against sharing gift items with loved ones, in fact, it is encouraged amongst Muslims. Prophet Muhammad said: "Give gifts to each other and you will love each other".
Still, the religion does not support Valentine's Day. One reason is the fact that Valentine, also known as lovers' day, celebrated globally on February 14, encourages casual sex.
Since the day also holds zero value on the Islamic Calendar, Muslim scholars all over the world agree that Valentine's Day is haram (prohibited).
New Year's Day
As mentioned above, any holiday or celebration that is not one of the two approved Islamic festivals - 'Eid al-Fitr and 'Eid al-Adha is not regarded since Muslims do not engage in any practice that is not established in their religion.
Allah says "'For every nation, We have ordained religious ceremonies which they must follow" (Q 22:67).
Based on this and the fact that New year's day has pagan origins, Muslims also do not celebrate this day.
It is important to add that Nigerian Muslims are currently trying to get the government to approve their own New Year's day.