Surely Custer would have preferred a few loud-mouthed injuns.....
Actually Custer was kind of stupid about that sort of thing. He had advance intel that there were large numbers of hostiles in the area of Little Big Horn and chose to disregard it.
The interesting one is Sherman. He was put in charge of the military district of Memphis early in the war. He went about gathering intel on the local secesh, who were loudly proclaiming themselves and had them rounded up and their property confiscated. Local sympathizers quickly figured out that STFU was a much better course of action. The rent of secesh landlords that was owed by renters was still collected by the military district, but then it was confiscated and turned over to the Union coffers.
