1. Are Muslims allowed to celebrate or join in other religions’ religious festivals and celebrations?

2. General Behavior With Non-Muslims
Islam is a religion of mercy to all people, both Muslims and non-Muslims.  The Prophet was described as being a mercy in the Quran due to the message he brought for humanity:
"And We have not sent you but as a mercy to all the worlds." (Quran 21:107)
When a person analyzes the legislations of Islam with an open mind, the Mercy mentioned in this verse will definitely become apparent.  One of the aspects constituting an epitome of this Mercy is the way the legislations of Islam deal with people of other faiths.
Not only does Islam demand their freedom to practice religion, but also that they be treated justly as any other fellow human.  Warning against any abuse of non-Muslims in an Islamic society, the Prophet stated:
"Beware!  Whoever is cruel and hard on a non-Muslim minority, curtails their rights, burdens them with more than they can bear, or takes anything from them against their free will; I (Prophet Muhammad) will complain against the person on the Day of Judgment." (Abu Dawud)

3. Continued…
Concerning behavior with peaceful non-Muslims Allah, may He be exalted, says (interpretation of the meaning):
“Allah does not forbid you to deal justly and kindly with those who did not fight against you on account of religion and did not drive you out of your homes. Verily, Allah loves those who deal with equity” [al-Mumtahanah 60:8].
In other words, Allah does not forbid you to be kind, uphold ties, return favours and be fair towards the non-Muslims, whether they are relatives and others, so long as they are not fighting you because of your religion or seeking to drive you out of your homes or trying to dissuade you from practicing your religion and your religious principles. So there is nothing wrong with you upholding ties with them, because upholding ties with them in this case does not involve anything that may lead to negative consequences.

4. Scholars Opinions regarding Celebrating Non-Muslim festivals with verses from the Quran and hadeeth of the Prophet Muhammad as proof

5. Greeting the kuffaar on Christmas and other religious holidays of theirs is haraam, by consensus, as Ibn al-Qayyim, may Allaah have mercy on him, said in Ahkaam Ahl al-Dhimmah: "Congratulating the kuffaar on the rituals that belong only to them is haraam by consensus…It is like congratulating someone for prostrating to the cross, or even worse than that. It is as great a sin as congratulating someone for drinking wine, or murdering someone, or having illicit sexual relations, and so on. Many of those who have no respect for their religion fall into this error; they do not realize the offensiveness of their actions. Whoever congratulates a person for his disobedience or bid’ah or kufr exposes himself to the wrath and anger of Allaah."

6. Congratulating the kuffaar on their religious festivals is haraam to the extent described by Ibn al-Qayyim because it implies that one accepts or approves of their rituals of kufr, even if one would not accept those things for oneself. But the Muslim should not accept the rituals of kufr or congratulate anyone else for them, because Allaah does not accept any of that at all, as He says (interpretation of the meaning):
"If you disbelieve, then verily, Allaah is not in need of you, He likes not disbelief for His slaves. And if you are grateful (by being believers), He is pleased therewith for you. . .“ [al-Zumar 39:7]
". . . This day, I have perfected your religion for you, completed My favour upon you, and have chosen for you Islaam as your religion . . ."  [al-Maa’idah 5:3]

7. So congratulating them is forbidden, whether they are one’s colleagues at work or otherwise.
These festivals are innovations in their religions, and even those which may have been prescribed formerly have been abrogated by the religion of Islaam, with which Allaah sent Muhammad (peace and blessings of Allaah be upon him) to the whole of mankind. Allaah says (interpretation of the meaning):  "Whoever seeks a religion other than Islaam, it will never be accepted of him, and in the Hereafter he will be one of the losers." [Aal ‘Imraan 3:85]

8. It is haraam for a Muslim to accept invitations on such occasions, because this is worse than congratulating them as it implies taking part in their celebrations. Similarly, Muslims are forbidden to imitate the kuffaar by having parties on such occasions, or exchanging gifts, or giving out sweets or food, or taking time off work, etc., because the Prophet (peace and blessings of Allaah be upon him) said: "Whoever imitates a people is one of them." Shaykh al-Islaam Ibn Taymiyah said in his book Iqtidaa’ al-siraat al-mustaqeem mukhaalifat ashaab al-jaheem: "Imitating them in some of their festivals implies that one is pleased with their false beliefs and practices, and gives them the hope that they may have the opportunity to humiliate and mislead the weak." Whoever does anything of this sort is a sinner, whether he does it out of politeness or to be friendly, or because he is too shy to refuse, or for whatever other reason, because this is hypocrisy in Islaam, and because it makes the kuffaar feel proud of their religion.
Majmoo’ah Fataawa wa Rasaa’il al-Shaykh Ibn ‘Uthaymeen,

9. Hadeeth on this issue
It was reported that the prophet PBUH said: In the days of Jahilia (Days of Ignorance, before islam), there were 2 days a year that people used to celebrate and when the Prophet PBUH came into the Madina, he said you used to have 2 days to celebrate and Allah replaced them with 2 days that are better, Al-adha and Al-fitr days. (Reported by Ahmed)
Another hadith says: A person who does similar acts to certain people he is one of them, and whomever loves certain people he is risen with them in the day of Judgment.
Those two hadiths (and similar ones) are the ones some scholars use to say that it is not allowed to celebrate other holidays.

10. Behavior with Non-Muslims
Ruling on celebrating others religious festivals:
Sheikh Salih:
Asim Hakeem: