The link below is from a homeowner in Minnesota who is outraged that her HOA has issued new rules against certain types of speech, like talking to your neighbor about the HOA board.
Can they really do that?
Well, yes they can. A private non-profit corporation can do just about anything it wants whether it seems constitutional or not.
A for-profit corporation can do the same. The Denver TV station where I worked for more than three decades had rules about private discussions between or among employees. Religion and politics were forbidden. Political correctness was mandated at all times.