The anti-institution sentiment is a result of them having clearly decided to move from attempting being apolitical to actively being political.
I don't see any anti-science sentiment here. If anything, conjecture is the first step to the process of science and the suppression of it within the institutions of science is very much anti-science. This is especially true when non-scientific institutions (liberal arts & soft sciences) pose as if their fields are grounded in axiomatic first principles like the hard sciences.
Now, I do agree that there is a rise in the loudness of conspiracies, but the previous century had a majority population that believed in creationism. So, I'm not sure if it is that much worse. Just that everyone has a megaphone now.
As far as conjectures go - it's always appreciated to make a hypothesis as long as you approach it in a healthy way. Science requires that you yourself try to disprove the hypothesis as much as possible before posting it to the world. Otherwise you end up with so many "takes" that people stop believing there is a valid answer and become apolitical and jaded. In time of internet and open access to scientific papers the tolerance for constant wild speculation should be very low.
"Science is the disbelief in experts" -- Feynman
By anti-science I would imagine you mean anti-expert.
This insane epistemological certainty is what is creeping in and far more dangerous than some crank who thinks the pyramids are 30k years old.
"I already know the results of the experiment so why bother"