For an example from the other side of the aisle, I opposed Steve Hsu being fired as VP of Research at Michigan State University in 2020 for his opinions, particularly regarding the genetics of race and intelligence (https://slatestarcodex.com/2020/06/16/open-thread-156-25/). Yet, ultimately, that was the risk of an administrative position such as his. He still is a full professor, and he has started several startups since then, so he's doing okay.
The main objection I have to positions like yours is that you believe that university administration should not be subject to pressure from politicians who grant universities the great privilege of being untaxed nonprofits with immense endowments and great influence in all the pillars of society. On the other hand, you believe that administrators should be subject to influence and control by left-wing student and academic protestors (I'm sure you think right-wing protestors would be illegitimate). I'm arguing that pressure on administration from both sides is legitimate, and that the former should flex its muscle more.
† I would also argue that academic fields that adopt activism as policy (so, all critical theory-influenced fields) should lose protection for their ideas, since they are clearly not pursued in a commitment to the truth, but that's a bit of an aside from my point here.
Go after the Churches and religious organizations first, in that case, as they’re also tax advantaged and their leaders and congregations have a profound pull upon politics and politicians.
I think the State should stay out of religion’s business entirely (that also means no “religious freedom” exemptions to treat others like second-class citizens that the evangelical right has been winning recently), along with universities too.
Leave both organizations tax-exempt, but they should not receive any public funds for any reason, nor get any other special protections from the government, lest there’s an explicit agreement to pay it back in the form of bonds or loans. Publicly-funded research at private institutions could remain the same as it is, with the caveat that results by-default should be public to all, rather than locked behind institutional paywalls.
(State universities are a valid edge case, but I’m specifically talking about private non-government organizations here)
That's the marketplace of ideas – not platforming every single idiot who wants to speak. Is Harvard supposed to, hyperbolically, entertain the notion of a flat earth if enough people believe it? I'd argue absolutely not (that's what the internet is for). Maybe the reason that the makeup of Harvard and similar schools is so liberal is because the right hasn't offered much in the way of intellectual fodder other than "Harvard bad" ?
If you don't agree with Harvard's policies, don't go to Harvard.
This one is intertwined with it:
https://en.m.wikipedia.org/wiki/List_of_law_schools_attended...
https://www.statista.com/chart/amp/24598/first-degree-colleg...
Expecting people to be consistent when it comes to treating organizations the same way is a fools gambit.
Why are they the best situated to speak truth to power?
Every academic knows that you have to "play ball" to get to tenure, and that's regarding the direct subject matter of your own scholarship. Electoral endorsements are practically the only form of outspokenness that cannot and will not be used against you, only because the courts would come down too hard on the institution.
Everything else is office politics!
edit: I would also note that the such actions by top administration imperils and has a chilling effect for faculty and student's contrarian thoughts and free speech. You you're not as likely to speak out against your boss/principal's ideas.