Crossing state lines means nothing. I could travel hundreds of miles and not cross state lines, Rittenhouse never left the general area his family lived in, the towns were adjacent to each other. The distance one travels to be there and what jurisdictional lines thay may have been crossed has no bearing on a self defense claim.
All four men involved in the shootings chose to go into "harm's way" and none of the four were law enforcement officers. And just like the distance traveled, it has no bearing on a self defense claim.
The only thing that mattered is that Rittenhouse had a reasonable fear of death or bodily injury. The gun could have been illegal (it wasn't), his possessing it could have been illegal (it wasn't), it could have been stupid for him to be there armed (it most definitely was) and it still would not negate his right to defend himself with lethal force if he reasonably feared for his safety.
There is video, forensic and testimony evidence that indicates the first man shot threatened Kyle, advanced on him and attempted to take his weapon. It at best establishes a reasonable threat and at worst establishes significant reasonable doubt on the murder charge.
There is video evidence of Kyle being hit with a skateboard by the second man shot while also being kicked in the head by a another man while on the ground.
The third man shot admitted Kyle did not raise his gun and shoot until after he drew and pointed a Glock pistol at him.
Which of the above three scenarios would you not personally fear for your life in?