So free speech is not a constitutionnal right if I follow your argument? You sound quite scary right now... (and I am not even concerned, not american)
Things become a bit more murky when you free speech while on somebody's payroll and representing them. Commercial speech has somewhat less protections than regular speech.
And anyway the first amendment is about the congress. It doesn't limit the capacity of the executive branch to do ideological purges as the McArthysm period showed. Although it did got limited by the courts - from the reading of case law it had to do more with the fifth amendment and not first.
The McCarthy era seems to be the time period when some people think America was "Great" and that we should return to it. I mean look how easy it is to label any policy as socialist/communist/marxist these days!
This neglects that prior administrations were often the origin of these demands, wanting to see how research impacted broader society. They were also, often enough, an ideological cover for the intelligence community to find US-friendly assets in foreign nations. Identity politics is an explicit soft power strategy of very many of the last administrations whose defence/intelligence budget funded some of this research.
The situation is vastly more complex than you imagine, and has far less to do with "woke administrators gone rouge".
The unstated target of much of this is the intelligence (, and defence to a lesser degree) community, which runs USAID, and plays a very significant role in research funding, and the like. The right has never been targeted in the way the left was, until Trump -- and many in his upper circle are now taking revenge.
This isn't about pronouns or land grants, no matter how hard that excuse is used. It is about Trump's administration destroying future decades of science, about dismantling the ability of the people to limit the oligarchs, about due process, about a respect for the separation powers that defines America's system of government, about the ability publish and communicate factual data about health, poverty, climate, and myriad other topics inconvenient to those currently in power.
Trump is president. He deserves every chance to reshape the government - but he MUST do so through constitutional processes. He is welcome to advocate for and organize legislation. He is welcome to advocate for and organize even constitutional amendments.
But his approach has wounded, deeply, a critical element of the rule of law. And once that disappears, we all lose everything.
