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 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.
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.