First of all, yes, private entities absolutely can ban you from speaking on their property. The 1A only restricts the government from jailing you. If we couldn't ban people from this sub, it would be an unreadable mess.
Second, the problem with the lefts cancelling is it was usually just a handful of terminally online freaks, digging through hundreds of tweets dating back years to find one example of a person saying "nigger", usually as a joke. It was completely devoid of nuance and purely vindictive.
The right is using it to get women who work with children fired because they're glad a normie was murdered. Does any normal person want a sociopath like that near thier kids?
The problem is always just the left, not the tools they use.
No. It does what it says it does.
That is in not restricted to jailing. They can't fine you. They can't limit your opportunities. They can't make any law that would abridge your freedom of speech. That includes any institution funded by the government, including colleges receiving government money.
I'm writing in shorthand because I'm on my phone at work but yes you're correct it's more nuanced than what I said