Depends on what the consequences are. Social alienation? Sure. Government intervention? Absolutely not.
For example, getting a college acceptance rescinded because of a racist statement.
If it's an institution that takes government money, it has no business going something like that.
What if it's a completely private college? Would it mean that college doesn't respect free speech?
Yes, and that is their right.
A lot of these institutions are putting their own credibility at risk by essentially allowing a heckler's veto of their admissions and other institutions.
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