I keep seeing this argument. You're using the word "shouldn't" to express your personal feelings rather than the law.
Now, to be clear, I agree with your personal feelings. But the solution is to change the law, not to be mad that it was applied correctly in this case.
He wasn't there to stop BLM. He was there to stop looters. It's deeply saddening to me that the two are synonymous in so many people's minds. There were looters destroying property and burning businesses for two days before the militia turned up. It makes no sense to loo at this case and rob it of that context.
Yes, Rittenhouse is keeping some very bad company. He's a dumb 17 year old with a hero complex. he may well be racist, who knows. But that has nothing to do with whether the case itself is about white supremacy.