That's another great question. You are certainly asking the right questions here, and, really, that's half the battle. The other half, of course, is being able to - as Aristotle(?) kinda said - consider an answer without accepting it as true.
So, is it? Is violence "just as bad" when it's done for reasons other than race?
You are judge, jury, and executioner.
You have two cases in front of you.
Case 1. Angry Guy in a bar sees a guy with a blue hat on and screams, "I hate blue hats" and beats the guy severely.
Case 2. Angry Guy in a bar sees a person of color and screams, "I hate people of color" and beats the guy equally as severely as in Case 1.
Do you punish them equally? For equal violence? Yes?
In the U.S., and much of Europe, they get punished differently. Specifically, they both get charged with assault, but in the 2nd case, the attacker gets charged with a "hate crime" and ends up with a greater penalty.
But, you ask, if they committed the same act of violence, for what is the extra punishment?
And, of course, the only answer is that they are being punished for their thoughts.
And if that doesn't scare you, the national debt is close to 20 trillion and the Fed is raising interest rates. Lol.