I've had to "shut up" many times in the classroom. The heat doesn't come from administration--it comes from the students. My evaluations tell me that students don't want to hear people who disagree with them--from the right or the left.
There are so many--TOO MANY--assumptions of how college professors are "indoctrinating" students. To be honest, we're not that influential. In reality, many aren't really paying attention. It's mostly the outliers that are causing the stir.
I want students to be free to express their opinions--just as long as they're informed ones.