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.
And only possible because of media and government pushing a hostile agenda. Otherwise nobody would've given a shit about a few unhinged twitter and reddit leftists screaming their heads off about someone saying nigger 10 years ago.