Correct. To the extent "hate speech" has legal meaning, it's that its presence in a defendant's history where they are accused of another crime (such as assault) could raise that crime to the level of "hate crime." A hate crime differs from a regular crime in that the plaintiff must prove that the defendant had a racially-motivated mens rea: they weren't transgressing against a victim for reasons such as personal grudge, but because they have a broad hatred of people in a category the victim is a member of and committed the crime because of that.

Saying "America is better off without black people in it" is not a crime by itself. Having a prosecutor dig up the Twitter post where you said that while you're defending a battery charge can turn a six months in jail / $2,000 fine crime into a one year / $5,000 fine crime.