You gotta be $hitting me :)
They're really popular in the Navy while we are deployed, and largely out of the public eye. People wear them on their foul weather jackets, which aren't really an official uniform item but rather gear that the command purchases. I saw dozens upon dozens of different morale patches last deployment. Sailors get them made up and often sell or trade them to each other. Many of these were very clever and funny. Lots of custom T-shirts as well that were made up and we could wear in the hangar bay when it's hot and we're allowed to take off our flight deck jerseys (only in the 5th Fleet AOR though).
Once we're back home, visible to the public, and wearing only official uniform items (no foul weather jackets), the morale patches are gone. They're very much a "what happens at sea, stays at sea" kinda thing.
I first saw this long after my time...
I seriously double if Uncle Sam's Misguided Children would have allowed me to wear one on my jungle utilities....
It would have made a great "Sniper Check", though!