IMVHO:
The covering of the female body and hair is not only a Christian issue. When I look at the area and culture the bible came from, I see it not so much as a "sexuality is scary" paradigm, but a "woman as possession" mindset. "Women as chattel" is a theme in the Old Testament, a book of which Christianity, Judiaism and Islam all have in their sacred documents. This culture keeps women covered and kept out of sight as much as possible, with only a few notable exceptions.
When I was hosting Saudi exchange students, I asked them why women were required to be covered up and men weren't. One student said that it was a matter of "protecting what is yours." He explained that no man wants another man looking at his women; they're his, and his alone. This dictum included not having a picture of any female relative in your wallet, lest another man looked at the picture and saw "your" woman.
I've also heard this couched in terms of "men can't control their lust when they see a woman's body or hair, so they have to be protected from their baser instincts," but if that were the case, men wouldn't be allowed to watch soccer together, because it might start them fighting over their favorite teams, which would be a "baser instinct" thing.
I think it's also a power thing; the more restrictions I can put on you, the more priviledged I feel. If someone from the subordinate class (in this case, women) has the same freedoms I do, then my status/power is threatened, unless I can explain the variation in non-favorable terms (a prostitute, a godless westerner, etc) and subject them to harsher treatment than other members of the subordinate group.
Of course, not all men of the desert culture feel this way; we're talking fundamentalists of all stripes here, and your milage may vary.

I think it's an overblown issue of modesty. I can understand some of the Muslim tradition that sounds like ownership and property where women are concerned. On the other side, looking at the fashion trends of the last 10 years I can see where a bit of modesty could be encouraged. There is a time, place and body size appropriate for crop tops. It's one of the reasons I refuse to perform as a member of a bellydance troupe. I refuse to shine my fat belly. I am a member of a troupe, by invitation. I dance for exercise, joy and other women, as is the dance tradition in the Middle East.

Female sexuality has only been in the forefront since the Women's Movement and Sexual Revolutions took off in the 1960's. The issue existed prior to that, but was less in the public eye. ... Trying to keep on topic, this could easily wander. Must think female sexuality and fundamentalism.....

My problem with being a church going SINGLE female is the attitude in so many churches. If you are single and over 25, something must be wrong with you! Yes, this is more region by region.