Why wouldnt coasties be military?
I think you’ve been watching too much “The Guardian”.
It is a sea going service with large warships, though perhaps not as large as the navy. They do focus more on law enforcement and homeland security but there are hundreds of overseas units. Some doing counter drug operations in the eastern pacific and gulf of mexico, some in the middle east as the first line of defense.. When navy boats are floating around over there guess whos right beside them in the battlegroup? Anyway.. coasties do a lot more than save drunken jackasses who sink there boats in america.