I never use my driver’s license when flying. My military ID is Real ID and my license isn’t. As for my passport and passprt card, they always stay in my carry on backpack that always goes on every trip.
I was stationed in Europe back in the late 70's/early 80's. The military ID allowed travel to most NATO countries. At some point anti US military protests started to take hold a bit as well the Red Brigades kidnapping a US general. I went to the local embassy and got a passport so I didn't have to flash my military ID to travel or rent a hotel room, etc.
That said: if I have to cary a passport for travel, it goes into a pouch that I wear around my neck...