Is this still true as it used to be? I of course see what you refer to, but I also know many highly intelligent and culturally literate people who are devout muslims and christians. Furthermore a lot of anti-intellectualism today is secular: flat earthers, people who call sugar "basically poison", anti-vaxxers, etc. I think this comes from a very different place: these theories/viewpoints distract people with a feeling that they're getting a look behind the curtain on how the world "really" works. And there is a good deal of overlap (think: tiktoker talks about the "secret code" they cracked in the bible) but I think these are distinct phenomena. I think the latter phenomenon is caused by low trust in society, I think, plus a hodgepodge of stuff like crappy faux-marxism ("every problem is just rich people", which although there is a grain of truth, does certainly not literally describe reality), laundered anti-semitism ("the world is actually run by lizard people cabals who are coincidentally jewish"), and new age speculation about stuff like mass psychosis. In fact i'd argue that "new age spirituality" seems to be a nexus for all of this (and curiously still overlaps with christianity), attracting both marks and conmen in crowds.
Or to put it another way, I don't see how Q Anon theories can be tied back to religion in any direct way, even if many posts do draw from antisemitism. I'd even put the "russiagate" stuff in this category—it's true that many of the allegations seem substantial, but feels highly disingenuous when AIPAC wields such naked influence over both parties. Surely by any metric that Trump is controlled by Russia, Israel's influence outstrips it by many orders of magnitude.
Tbh, some of it is also just inability to interpret media. Particularly coverage of politics. Watching cable or reading opinion columns you'd think the parties were diametrically opposed and represent two wildly different aspects of america—when it takes about half an hour of reading a sampling of how politics works in other countries to realize how similar our parties are compared to basically every other party system on earth (excepting Britain, I guess?). Interestingly, for a country that prides itself on voting and political opinions, we're actually quite terrible at ceding the conversation to "experts" who are often even worse-informed and less educated than many of us.
Chomsky has this great bit about how Americans will call into a baseball show as an expert to criticize everything. The coaches, tbe players, etc. most of these people don't play baseball at all but feel very confident and passionate. He then points out how those same people will not have opinions about how government should work and leave criticism and demands to "pundits" even though they are much better equipped to figure out if they are being represented well than they are to judge the performance of a professional athlete. I think the internet cracked that open and now everyone has opinions. I'm curious how much anti-intellectualism just comes from democratization of public discourse and little has actually gotten worse, we're just more aware than we were before.