Compelled speach and compelled listening is not free speech. It is one thing to have to attend training on safe welding practices or safe coffee pot operations if you are in the federla government. It is quite another to have to take training to teach you "safe" political opinions in the workplace. It is a page right out of the disinformation training manual 1984.
As Yogi Berra was reported to say, “Take the man’s money, take the man’s guff.”
We have many 1st Amendment and other Constitutional rights, none of which give someone the right to a particular job.