Because society is based on the idea that Deities exist in a spiritual rhealm somewhere "out there" and intangible, and the idea that the beings in these craft could be real, and might PRODUCE Deities and semi-deities (Gods, Goddeses, Demons, Jinni, Angels, whatever), would utterly shatter the worldviews of the religious people that have been taught for millenia that those deities are spirits, NOT that they fly around in technological craft and are NOT spirits and advanced robotics instead.

People think religion will survive disclosure of whatever these beings are (Cryptoterrestrial, Interdimensional, Aliens, Other explanations), but I don't see how it could... Society and political power is based on religion as management of anyone outside of the upper class, their worldview will be obliterated if disclosure happens.

I'm talking the Pope turning into a Scientologist and all the Church Canon Law getting overthrown overnight type smashed, governments getting overthrown type smashed, etc. The government may not be actively "lying" in any non-compartmentalized way to "The People", but "The People" will assume that compartmentalization doesn't really exist and everyone in government knew and covered it up, and then proceed to overthrow the government, because if the government could cover THAT up, then suddenly every other conspiracy theory becomes plausible and magnified in their minds, and due to not believing religion anymore due to realizing it was a deception given to them by these beings, they will naturally lose all faith in religion and government.

Anthropological principle is what it is called. There will be no disclosure unless those beings want there to be, and even then there could be very very few ppl in government that are significantly aware of what's going on, due to compartmentalization.