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!
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.