I have been playing this game for some time, finished the main story with the institute. Started a new save and did a lot of extra questing. (So much that Kellogg was dead with 2 shots )
But i was wondering, is you go with the institute, you come across a mission where the institute tries to pick up a scientist. And the Minutemen try to stop that from happening. During my last playtrough, I managed to resolve the matter peacefully.

But what happens when you decide to just kill the Minutemen? Has anyone done this? What are the repurcussions of this? Can you no longer go to your settlements?

Well, you can lose Preston if his approval goes too low.