Wa `alaykum as-salamu wa rahmatullahi wa barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Brother, we really appreciate your forwarding this question to us, and we commend your keenness on getting yourself well-acquainted with the teachings of Islam. May Allah help us all keep firm on the Right Path, Ameen!
As far as Islamic Shari`ah is concerned, a Muslim is not allowed to participate in any religious aspect of a celebration that is related to non-Muslims. However, we should not forget our role in society. We should be good examples to others. Islam urges us to be kind to everyone without any kind of discrimination due to differences in faith or race.
In his response to your question, Sheikh Mohamed El-Moctar El-Shinqiti, Director of the Islamic Center of South Plains,Lubbock, Texas, states:
Most jurists that are specialized in fiqh of Muslim minorities and are aware of the cultures of western societies tend to agree that celebrating non-religious feasts, such as Independence Day and Labor Day, is not forbidden. However, most scholars forbid celebrating religious feasts, such as Christmas, while others, such as Sheikh Ahmad Kutty and Dr. Jamal Badawi, permit new converts to attend their family celebrations without participating in anything that is purely religious related to these celebrations.
It is difficult to categorize certain feasts like Thanksgiving and New Year as religious.
Generally speaking, we can say that it is forbidden for the Muslim to participate in any religious aspect of a celebration, except the Islamic celebrations of the two `Eids, and it is allowed to take part in the general, non-religious aspects of the celebrations of other feasts.
In this context it is important to note that congratulating non-Muslims on their religious or non-religious feasts and exchanging gifts on these occasions is part of the good relations that we are commanded to keep with them. It is also a practical example of the concept of 'birr' that Islam has emphasized when it comes to Muslim-non-Muslim relations. This is especially so if the non-Muslims congratulate and exchange gifts with us on our Islamic feasts.
Allah Almighty knows best.