that is precisely where you don't want them. you want to do anything you can so as to not be easily recognized as an American. Big Blue Flight Safety Tags in English that say CREW on them are a dead give away.
i don't understand what you mean when you ask "what do you do overseas?" we go all over the world with no issues. We try not to stand out. We wear no uniforms, no crew tags. all wear different clothes. different ties etc. no badges until we need to show them at the airport. simple things.
Amen bruther- don't stick out. Anything that can be done to stay off of the radar is mandatory. Crew tags, uniforms, etc. Don't look like a pilot and blend in. Stealth.