Can HOAs punish homeowners for bad reviews?

An HOA in a Gilbert neighborhood sent out letters threatening to fine people $250 per day for negative posts and even revoke their privileges to common areas.
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"12 News: It's a Matter of Facts"

[marilynv]

HOA should be sued for violating their constitutional right of freedom of speech in any form whether written or verbal on a platform.

[juliemathias]

So if your going to say something bad about the hoa or where you live, just remember always say “ I my opinion “ and it’s not deformation.

[brucegrzegorzewski]

First our dues repeesents a purchased right. The HOA works for you not the other way. Comments and opinions are an everyday exchange.

[Catmomma]

But its your own fault for dealing with and buying a place with an HOA.

[DieseltheGermanShephard]

Comment under a FAKE NAME, they can't trace it back to you!!!