As a Muslim woman, I dress modestly, covering to throat, wrist, and ankle and wearing a headscarf, when I'm outside my home. I observe hijab as an expression of my religious faith and have since I converted to Islam 14 years ago. I've worn hijab so long that it feels like a natural part of who I am and I usually don't think too much about it these days.
However, as I've come to explore my asexuality in recent years and to understand what it means for me, I've come to realize that part of what I like about hijab and part of why I think it feels so natural to me, is that in my experience it does desexualize me in the eyes of most people and that this makes my interactions with them more comfortable for me. While this doesn't necessarily hold true for everybody, it has for me.
For me, hijab is a way for me to opt out of the expectations sometimes placed on women in our society to be sexy and attractive to men. It's also a way for me to opt out of a lot of things that are considered "girly" or elements of conventional femininity, like fashion, makeup, hairstyles, jewelry, and so forth. These are things I've really never gotten in the way that most other women seem to, and was never into even as a teenager, long before I converted to Islam. Wearing hijab doesn't necessarily mean you have to give up on these things, but it can, and it's become part of the whole thing for me and is another reason why I think I'm so comfortable with it.
In my experience there isn't a stereotype that hijabis are asexual - most of the stereotypes relate to being oppressed, being foreign or "not American", and so forth. I'm white and one of the most common assumptions people make is that I dress like I do - and even that I follow my religion - because a Muslim husband made me (I am not married and never have been, nor do I plan to). Maybe if I were a nun and dressed like one people would associate my appearance with something about asexuality or celibacy, but the ideas our culture has about Islam completely override that.
It's curious that although people don't take my hijab to imply asexuality, I find that it does in fact suit me well as an asexual.