That’s what makes this quite a bit different than your gun analogy.
Someone yelling fire in a crowded theatre isn’t “automatically assumed to be guilty”, they’ll be charged and placed on trial and the state will have to prove that a) they yelled fire, and b) this was the kind of speech we agree isn’t protected because it’s intended to cause harm. Similarly, if i’m caught possessing hate material the state would charge me and have to prove that i did possess that material, and that material fits the definition of hate speech.
Thinking genocidal thoughts, even saying genocidal ideas aloud, all are ok under most western hate speech laws. The line is usually in publishing or broadcasting genocidal ideas.
Hate speech laws are on a slope, and at the bottom is of that slope is authoritarian thought police territory, for sure, but it doesn't seem that slippery a slope from where i’m standing.
So everyone has hate speech and the government can selectively choose who to prosecute. And just the act of defense is punishment enough, so the law is bad on that account.
If everyone in the country has an illegal gun then the law would be similar. In this case the law is not properly able to be enforced. In the US this would render it invalid.