Hate speech is part of Free Speech and assuming that words can beas hurtful as acts is trivialization of actual violence. You can be offended by what someone is saying but yuo have no right in shutting them down.
I agree with you when you say that neutral laws generate inequality and I am surprise that this seems “unffair” to you, as if a society of free individuals equires a 50–50 in everything. When you say that some people might be intimidated by “hate speech” and thus not express their ideas, that’s their fault, we put ourselves in boxes so that a “progressive” stack can be implemented.
Ps. The persone you quote at the beginning is wrong