From the Soviet Union? Nope. Cuba? Nope. Venezuela? Nope. Three strikes. You're out.
From the United States Air Force materials on Combating Extremism in the Air Force:
Apparently there are things you aren't allowed to watch, things you aren't allowed to read, ideologies you aren't allowed to study, and things you aren't allowed to say or mention.
Seems like branches of the government may be confused about that whole pesky 1st Amendment thing. Yes, you give up some of your rights when you sign up with the military, but pretty sure you don't give up all of them, possibly including reading books on your off time or talking about "impermissible" ideologies.
On the other hand, if we are going to go this direction, I assume our current overlords will have no issue with the current list of impermissible ideologies being replaced with Marxism, communism,socialism, and progressivism as impermissible.
Read a longer post on the topic over at Dr. Phi's page.