Is it permissible for a Muslim woman to allow her four-year-old daughter to attend the birthday party of her non-Muslim friend?

An Islamic school should be chosen for the daughter, if available, to avoid the corrupting influences of foreign schools at this critical age, for the daughter is a trust and a responsibility. Celebrating birthdays is an innovation (bid'ah) and an imitation of disbelievers, and it will be rejected from its doer. It was not part of the guidance of the Prophet or his Companions. It is not permissible to let the daughter attend these celebrations. Friendship, kindness, and benevolence are permissible with non-Muslims, provided there is no heartfelt affection for them, and provided this relationship is utilized to invite them to Islam.