i personaly cant wear a wrap on my head because of my glasses and the fogging it causes...
In that situation, you should play as US then because if it's around your neck and you are wearing a hat, it looks like you are playing as a US person. If there is an aspect of one specific side that you can't meet, switch sides
theres also diferent ways that you can wear a shemaghe, in the standard wrap it can serve 3 purposes: full mask, hood and collar. Pulling the hood back over your head and using it in the collar setup would have been sufficient to stop serious fogging.
QFT. Theres a variety of ways to wear it, try wearing it like a giant headband across your temples like I was. No fog problems at all, and it's still blatantly obvious that I was taliban
OR you could wear it as a turban and look cooler than anyone else out there