This reminds me of a funny story that happened when my father was working in Abu Dhabi (same country as Dubai, different city). I was around 15, then, I think?
Anyway, I was walking over to my friend's place, and I'd wrapped a scarf around my head to keep the heat off. Suddenly an older lady suddenly took ahold of my arm, led me aside, and started scolding me in broken English mixed with Arabic for doing my scarf so messily that my hair was visible.
She wasn't angry or yelling or anything, just sort of tutting and fussing like a mother hen while busily re-arranging my scarf for me. I have to admit that when she was done it looked really nice, with the pleats being all neat and straight. She gave me one last look, nodded her head in satisfaction, and then bustled off into the busy street.
It was the weirdest encounter and I honestly didn't know what to think. Later my friend and I decided that, because of my ethnicity and the way in which I'd tied my scarf, the lady had most likely mistaken me for a Muslim girl. That's probably why she had felt the need to jump in and help me. It was weird at the time, but in hindsight it's kind of funny and I got a pretty scarf pin out of it.
Not to scare you off Amanita. Generally as long as you are dressed relatively modestly people don't look twice at you, especially if you are obviously a foreigner. It's just that the talk of Dubai and head scarves reminded me of this story.