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.
I do not ever remember a time when it was socially acceptable to cheer on a political assassination.
If this had happened 20, 30, 40 years ago, people would have been fired, ostracised by friends, family, etc.
Cancel Culture was getting people fired simply for disagreeing with the left wing. Openly celebrating a murder is an entirely different thing and would never have been okay before the words "cancel culture" were even in the public dialogue.
It's pure and simple gaslighting to continue the comparison.