I think in the world of the movie, a thing like that would be suicide, yes. In the real world there are "free speech" fictions that need to be kept up, so likely he'd be fired. It's possible the film was trying to meet halfway the real world and the fascism of the film uiniverse, so the bit about the Koran was addded as a ficticious incentive for calling him a traitor and killing him. That is, we want to kill him for that show, so let's look into him for an excuse. Of course having it be the Koran at all was an effort to update the story to the politics of today.