Is it permissible to congratulate one's mother on her birthday if she is far from religious observance, knowing that celebrating this occasion is forbidden, and fearing her alienation?

A person celebrating their birthday is an innovated bid'ah (religious innovation) and an imitation of disbelievers. Congratulating others on it is also participation in this bid'ah and an imitation of disbelievers. Allah Almighty says: (And cooperate in righteousness and piety, but do not cooperate in sin and aggression). Obedience to parents is obligatory, but it is not in disobedience to Allah. The right of Allah takes precedence, and there is no obedience to a creature in disobedience to the Creator. Allah Almighty says: (But if they endeavor to make you associate with Me that of which you have no knowledge, do not obey them but accompany them in [this] world with appropriate kindness). Therefore, you must politely explain to your mother why you are not congratulating her on her birthday, and continue to honor her and treat her kindly in matters that do not violate Islamic law. Among the greatest acts of kindness is to supplicate for her guidance and be eager to invite her to adhere to Allah's law, and gladden her heart with gifts, kindness, and good treatment.