Something I think is important to remember about the 'crossing state borders' thing is that Kyle Rittenhouse lived in Antioch IL, which is on the very northern tip of the state and actually only about half an hour away from the sight of the protests. Looking at Google Maps, there's less than a mile break between the two town's suburban areas.

This kid pretty much did the equivalent of driving from Carrollton to Dallas, it just happens both cities sit on opposite sides of a state boundary.