brigade quartermasters shemagh I think so long as you aren't wearing the traditional red or blue checkered on white shemaghs you should be okay. The link above is for the type sold to our soldiers in Iraq and Afganistan and I have a couple of them now. They are lightweight and comfortable, and I wear them a lot when I fly. I use them as scarves in mild weather. I usually just wear them as a neck wrap most of the time, though I've worn them combat or desert style more than once. They make a great head wrap for sleeping in the bush at night.
While I was in Baghdad I got talked into wearing one combat style by a local girl working for us, and I entered a work area where a few local Iraqis were. I had on khaki pants and a black tee shirt, and when I walked through the door, you should've seen the look on some of their faces. I promptly removed the shemagh so they didn't get too set off by it, and they seemed okay then. I swear some of them must've thought they were about to lose their heads.
As a scarf, I doubt anyone is going to even care. Wearing it combat style amongst the public you will get much unwanted attention. Unless there is a big dust storm in your location at the time, there is not much need to be wearing it that way anyways. Draped over your head with your face exposed may seem unusual, but will not be quite so alarming to others.
The BQ site has a link to instructions on how to wear the shemagh combat style. I learned an improved variation that is neater and more secure than what they show. Their size is pretty typical of what the MEs use. If you get an egal(the ring for the crown of your head) you can were a shemagh like a more traditional head dress
brigade quartermasters shemagh