This is a matter of real scholarly difference. A number of scholars, particularly from more conservative traditions, hold that Muslims should not participate in the religious festivals of other faiths because doing so may involve resembling or affirming beliefs and rituals tied to another religion, citing the hadith 'Whoever imitates a people is one of them' (Sunan Abu Dawud 4031). On this view, Islam already provides its own two major celebrations, Eid al-Fitr and Eid al-Adha, and Muslims are encouraged to be content with these rather than adopting other religious occasions. Other, generally more contemporary scholars distinguish between the religious content of a holiday and its purely social or cultural trappings, permitting things like attending a non-Muslim relative's birthday gathering, exchanging gifts, or being present at a festive meal as a guest, as long as one does not participate in specifically religious rites or affirm beliefs contrary to tawhid. Birthdays for oneself or one's children are a separate, less contentious issue: many scholars permit simple celebration as a cultural custom, while others avoid it out of caution regarding religious innovation (bid'ah). Given this range of opinion, Muslims are encouraged to consult knowledgeable local scholars and consider their specific family and social context.
Q&A · Rulings
Is it permissible for Muslims to celebrate non-Islamic holidays or birthdays?
References
Sunan Abu Dawud 4031
Informational, not a personal fatwa. Consult a qualified scholar for rulings on your situation.