All good points. I should clarify that when I say "anti-intellectualism" I don't mean "being stupid" but rather the more systemic issue of people being propagandized into distrusting the concept of basic institutions, to the benefit of reactionary forces. "Do your own research" isn't really skepticism, it's a more fundamental rejection of reality. There's a difference between being critical of prevailing institutions or ideas, and being skeptical of the idea that these institutions are legitimate in the first place. Even Marxist critiques of economics are made in the context that the academic institution overall has some merit (or else there would be no reason to be critical of economics, specifically).

I think the ancient aliens stuff is sort of the sillier end of that more general rejection of reality. It doesn't really matter if you believe in it or not, but it comes from the same place, which is a rejection of some basic assumptions that most of us do take as given. My guess, if I could make a better attempt at answering your question, is that it's a low-stakes way of testing the waters with people about their willingness to challenge the more substantial baseline assumptions about reality. You put out an idea that is both unverifiable and irrelevant, like Jesus being an alien, and you plant the idea that there could be other things that might be wrong about what the established institutions say about things. Then you leverage that wedge of uncertainty into getting people whipped up about whatever your actual ideological goal is. More importantly, you do it in a way that undermines people trying to accurately describe the world, because accurately describing the world goes against reactionary ideology.