Is he who believes in the permissibility of calling the holidays of the polytheists "Eid" an infidel? And is what is meant by that he who believes in the validity of their beliefs? And does this ruling apply to other innovated holidays such as the Prophet's Birthday (Mawlid), the Hijri New Year, and the Gregorian New Year?

The difference between believing in the validity of calling something an 'eid' (festival) and believing in the validity of the content of the 'eid' is clear. The first is correct, and the second is false. Calling the festivals of the polytheists 'eids' does not mean approving of their content. Indeed, the Prophet, peace and blessings be upon him, said: "Every nation has its eid." And he would fast on Saturdays and Sundays to differ from the polytheists. An 'eid' is something that is accustomed to coming and being intended, in terms of time and place. Allah Almighty has made for Muslims the two Eids of Fitr and Adha, and the days of Mina, as a substitute for the temporal and spatial festivals of the polytheists. Celebrating polytheistic festivals can be an入口 to disbelief, whereas innovation (bid'ah) falls under matters of what is lawful and unlawful.