As far as I'm aware Rittenhouse was acting within his legal rights.
Here is a really good summary from someone with two degress in criminal justice:
https://www.youtube.com/watch?v=dfAz851P8p4
The fact you used the "carried a weapon across state lines" line suggests that you may be consuming biased reports. It's not a crime to carry a weapoon across state lines. He also lived right on the state line and worked in Kenosha. It's not like he drove miles to shoot protestors in some city he has no affiliation to and portraying it like this is dishonest.
He also probably acted within self-defense as is covered in this part of the video I shared:
https://www.youtube.com/watch?t=648&v=dfAz851P8p4
For the record, I think what he did was reckless and dangerous, but the catalyst to this was the riots and looting. Right or wrong you'll find some people will react like this when they feel their neighbourhoods are under attack. You can't expect one group to be violent without some kind of push back from another. The same problem exists with antifa and BLM (not that these groups are a direct comparison). My point is these groups don't exist in a vaccum, they appear when they believe law enforcement and those in power are not doing a good enough job. You have to go a level deeper and ask why BLM protestors are on the street, and why are people are feeling the need to form militas in the first place? If you ignore the causes these events will continue to occur and likely escalate.