Okay, you've typed a few long posts, ill attempt to answer in one.
Yes, professors have opinions, and yes their job is to "open minds to new ideas". Opening minds is not teaching one side of a debate though, as has been my experience. But I still dont think thats "indoctrination", or maybe its a small part of it.
Teachers and professors can absolutley "coerce" rather easily. Choice of topics, assignments of papers (you will write about how X influenced your life, even if you dont believe X exists). Choice of novels to read and report on. (This is a blatently obvious one in my and my children's experience. )Administrators supporting school walk outs for only one side of a debate, etc. Teachers getting kids to transition and helping hide it from parents. (In California, there are actual laws assisting that now, and maybe other states too.)
Coercion could be grading harsher for not aligning with certain opinions. Many have claimed this, but it is almost impossible to prove.
As for the teachers getting dismissed immediately for trying to transition kids? I know of one example from a greenville middle school maybe 4 years ago involving several girls whose parents pulled them out of the school. The teacher was not dismissed, but i cant say if she was disciplined. I could find no public record of any punishment.
I also just spent time with a grade school teacher in Indiana who has a litter box in one of the other teachers rooms for a furry student.
I have to ask, and I dont intend it as confrontational. First off, everyone thinks they themselves as middle if the aisle politically. We're always normal and everyone further right and left are the extremists.

But how would your friends and family describe your political leanings?
I ask because, if a teacher is pushing a political idea that I agree with, I am far less likely to consider it indoctrination, and would probably not be as quick to notice the lack of balance. If its an idea I disagree with, I am far more likely to recognize the imbalance. And with teachers unions, teachers population, (and especially professors heavy lean left), I can easily see people who even lean left not really seeing an issue, while being honest about it.