It would be interesting though to see if aliens find different contortions on which to base religious beliefs. Like, a stable equilibrium of people pretending to see what their religion asserts and avoiding signalling

That occurs in some human religions also just less commonly with sight but rather other observational claims. For example, in some forms of Protestant evangelicalism it is uncommon for people to talk about all the terrible things they did before they accepted Jesus as their personal lord and savior. Very few of those people were the drug-fueled, alcoholic, decadent, Satan-worshippers that they claim to have been. But no one calls them out on it.