You are attempting to frame state controls on speech as some form of "liberation". This is quite literally 1984 "Freedom is Slavery" kind of thinking.
Defamation and libel laws are a classic example. They are an infringement on an individual's right to free speech. However we as society have decided that is justified when that speech is being used to infringe on the rights of another person. Hate speech laws are basically the same thing as defamation and libel laws except they are scaled up to protect groups of people instead of just individuals.
Whether these tradeoffs of one group's rights for another group's rights are worth making is certainly up for debate. However it seems pretty obvious that hate speech laws do serve to provide liberation and freedom for people who would commonly be the recipients of hate speech.