No.
> For example, suppose someone says "I think that everyone who does not believe in my religion should be killed." That type of speech is intimidating and comes with the threat of violence. Therefore any non-believer might pretend to believe and censor themselves out of fear for their lives. In this way, the speech itself acts as a form of censorship, and allowing it to occur silences more people than banning it.
You are conflating things. Hate speech isn't about threats of violence.
Hate speech is when you have specially classified groups of protected people that you are not allowed to offend or mock or belittle. It is also about making it illegal to talk about subjects that are not approved by the government. Like how you are not allowed to show nazi flags in video games.
You can go ahead and offend, mock, or belittle people that are not part of a protected class. That isn't illegal under "hate speech laws".
Nobody is defending or claiming that threatening people with violence is "free speech". Trying to claim this is grossly misrepresenting the entire argument. Either for, or against, hate speech.