I believe I understand your perspective, but there's a few things being conflated here.
Regarding the example you provided wherein the professor was fired from her job:
- You're entitled to your own opinion, you're welcome to publish it, etc.
- Your opinion can be bad and others may dislike you for it. That's fair. You are not free from repercussions.
- A tenured professor is a representative of their university, an employee. They are a face of the school, they teach classes, etc. As far as I'm concerned, no employer should be subjected to bad PR solely because of your shitty opinion. If they want you gone, tough, that's what you signed up for.
- It sounds like the university took this seriously and launched an investigation. Seems like the right thing to me. No one should be subjected to an environment where they do not feel safe or comfortable, let alone paying university students. How should an Aboriginal student feel?
Next, the fact that you see very little difference between opinions on racism and corruption in this example is pretty concerning. For one, race is a protected class, but like birth gender, sexual orientation, etc. affects everyone. It's an intrinsic part of the individual, the identity. A more apt comparison might be "Canada is NOT sexist" which I don't think would receive a response surprising to anyone.
I don't think any individual stance on corruption, at least in North America, could be considered remotely controversial. Except, maybe, to people who have been personally impacted by corruption, which I imagine is a small cohort, but the same would apply for practically any topic.
Looping back around, I dislike the notion that "it's right to cancel" anyone. We're not executing people without trial. People aren't (usually) going to jail or dying. In your first example, it seems the professor chose this hill to die on, instead of apologizing or attempting to show some empathy. Their choice.
The mistake you and others here frequently make is that people are not logicians in isolated environments. People are emotional, have vastly different experiences and varying degrees of education, and a variety of communication skills. Life, or Twitter, isn't a structured debate, even if you'd like it to be. If you piss a lot of people off, you're going to have a bad time. The very connected world in which we live changes things. If you have a controversial opinion that might piss people off, maybe don't share it somewhere easily discovered by said people. Or better still, maybe consider why they might be pissed off and reflect on your choices.