Flip it over: if you worked for Apple and wrote and circulated an open letter criticizing Tim Cook's advocacy of LGBTQ rights, what would happen?
I bet you'd be fired.
I said the same thing by the way about the guy who got fired from Google for circulating a misogynistic rant about female engineers. That was also stupid and unprofessional at the very least.
Politics at work can be generally problematic. Political rants at work that criticize leadership or coworkers or are broadly offensive are probably going to get you fired.