What is the ruling on attending an invitation for dinner at a friend’s house without it being clearly stated that this occasion is for the birthday of one of the family and without any congratulations or mention of the birthday, but the only problem is that the day of the invitation is the birthday and there will be a cake after the dinner?.
It is not acceptable to celebrate the birthday of anyone, because if that is done as an act of worship in order to draw closer to Allaah, it is an innovation (bid’ah) because it is not mentioned in sharee’ah. If it is done repeatedly, as a habit, then it becomes an innovated festival or eid, and an imitation of the non-Muslims from whom these celebrations have been taken. See the answer to question no. 1027.
If a person is invited to a meal and he knows or thinks it most likely that it is a celebration of the birthday of one of the people, then it is not prescribed for him to attend, because his attending is approval of the evil deed and helping in it. Allaah says (interpretation of the meaning):
“Help you one another in Al‑Birr and At‑Taqwa (virtue, righteousness and piety); but do not help one another in sin and transgression. And fear Allaah. Verily, Allaah is Severe in punishment”
See also the answer to question no. 9485
And Allaah knows best.