I am a non-muslim, and I wore a Hijab yesterday and walked around the city. Not to prove something, it was purely by accident. I had a kashmir scarf and I had a bad hair day, and I had no time to do my hair so I decided to wear the Hijab. Here is my experience.
It felt like I was being watched... people frowned, some made remarks behind my back, some western woman looked down on me, two Muslim woman smiled at me, and men were more polite, and I received no catcalls. I felt that some people gave me more respect, and others immediately stereotyped me.
I did not realize the effect it would have on me. When I walked around with a hijab, I felt very comfortable. I did not feel any pressure to look good, did not worry about my hair and since the weather is cold here, I felt very warm and comfortable. I got used to it very quickly, and when I noticed woman without hijab I thought: girl, how do you protect your hair from the wind and rain? wear something! haha! I might incorporate the Hijab into my daily routine, especially when it is cold. I mean no disrespect, since Christian and Jewish woman also wear/wore some form of hijab, although it has another name.
I found some new respect for Muslim woman who wear the Hijab. I "get" it now.