I tend to be on the conservative end of this issue, so I mostly agree with you. However there have been some notable instances of people getting fired for expressing left-wing viewpoints - the ones I can recall were college professors.
So the door does swing both ways, but I do agree that the majority of "cancellations" nowadays are coming from one side.
27% of transgender workers reported being fired, not hired, or denied promotion in 2016-2017 [2]. That's ~530,000 people [1], and really just the tip of the ice-berg. Until like 2 weeks ago that was completely legal federally, and in the states where it's most prevalent.
Three of my high school teachers were fired for being gay. One of them was outed by a parent who lived next door.
I was fired from my first job (at a secular for-profit company) for not tithing.
High-profile social media blowups are really trivial compared to the work-a-day homophobia and borderline theocracy that pervades vast swathes of America's land mass.
This is where I sort of miss the boat on the concern about cancel culture. Yes, those people shouldn't lose their jobs for expressing themselves. But also, where the hell has all this outrage been while LGBT people have been systematically excluded from any public-facing employment in huge swathes of the country?
"Cancel culture" is orthogonal to the issues you're describing, I think. Professional and social life is very unfair for people across many spectra of belief and being, sadly. I'd argue there's been growing outrage about both sorts of phenomena in the past few decades.
If some sort of culture deems you impure, you're likely to be outcast. Different people just happen to run up against different cultures.
Discrimination based on immutable attributes is inherently much more unfair, but unfairness is still a battle waged on many fronts.
Right-wing entities appear to sack people for left-wing views without external pressure, neutral entities are forced to sack people for right-wing views.
In regards to opinion safety the answer is clear: you don't get fired in a twitter shitstorm for expressing left-wing orthodoxy.