First, I do as Tousi. I approach people in uniform. I tell them I'm a veteran and deaf, then say and sign, "Thank you." Many respond with variations of ASL "You're welcome." If some have time, we shoot the breeze.
As to the controversy. I understand it, but I think it's a tempest in a teapot. All people take up handsigns, and few even think about ASL when they do.
Close to this instance are military combat signs and signals.
Common civilian signs mimicking ASL but are mere coincidence are . . .
Thumbs up. Our sign for ten, but means "all right" or "way to go" to most hearies.
Our F hand. Hearies use it for "Okay."
Our R hand. Hearies use it for "I hope" or "good luck."
Ha ha ha, when I was in Germany, I used the T hand for something, and a man told me that was a local sign the same as showing the middle finger.
The list goes on and on. If everyone had to check with the king and queen of ASL, then they'd also need to okay signs with all the different native tribes whose sign languages predate ASL.