Conservatives exaggerate, but liberal bias is a real problem in universities; three factors underpin this.
I subscribe to a weekly update on recent cognitive science papers. Over the past 12 months the research has eerily focused on correlating things like dark triad personality traits with support for Trump. One recently measured implicit racism and disparagingly referenced 'colour blind ideology'. These papers appear to be highly political and not very scientific.
> there are countervailing trends; most academics remain tolerant
The paper you link to with the word "tolerant" says this:
"findings from all surveys essentially conform to previous studies of soft authoritarianism that uniformly find a) a strong left skew in the professoriate; b) significant political discrimination against conservatives; and c) chilling effects and self-censorship ..... With such a consistent density of work replicating the same results, those who refuse to recognize the reality of political discrimination and chilling effects are not dissimilar to those who initially denied the leftist makeup of the professoriate (up to the 1990s), or who say that the earth is no warmer today than it was a century ago ..... Findings accumulated over a decade convincingly show that a majority of conservative academics experience a hostile environment for their beliefs in US, Canadian, and British universities. This is a rational appraisal of the significant structural discrimination against them in the higher education sector."
How did you get from this to "most academics remain tolerant"?
The other paper you cite is hard to interpret because, at least in the PDF I was served, all the tables of data are missing. The caption of the table remains but no actual table is visible. That seems like a problem. The paper is claiming that of the tiny minority of conservatives who remain on campus, they are about as satisfied with their career or a bit more than the rest. This is then cited as evidence there's no discrimination! That seems like rather ridiculous logic. Yes if you get rid of everyone who disagrees with you then the ones who are left won't see any problems, this is tautological. To understand if there's been discrimination against conservative academics you'd need to interview the ones who have left, not just those who remain!
If this is the best evidence you have that conservatives are exaggerating, then universities are truly doomed.
Is this a factor though that conservative views have started to lean more towards conspiracy theories and religion vs fact and science? I would also say debate never really changes anyone's minds. People tend to believe things with emotions and believe irrational things even when showing overwhelming evidence. This happens on both sides of politics or anything.