I have struggled with the question of religion in the past since it appears to me that most of those I have encountered appear to be set up along and defined by patriarchal society. I am not religious in any way, although I did dabble with "born again" Christianity in my teens.
However, I have come to understand thanks to many of the fabulous religious people on MN and other parts of the web, that many feminist women believers separate and distinguish between the god they worship and the institutionalised structure and/or some its theology. I have heard it argue that patriarchy has deformed and manipulated their religion and they see their goal as overcoming this.
It makes a lot of sense to me in that I have always been interested in the messages attributed to Jesus in the bible. I find I agree with much of what he appears to say. However, I dislike intensely how the Christian Church evolved and formed into a patriarchal institution which systematically erased and denied female participation and overlooked and/or rewrote much of what Jesus appeared to have said in order to make it fit in with their worldview. If I were to believe that Jesus was infact divine (which I don't) I think it would be perfectly possible to be the same feminist I am and be a Christian, iyswim. It would just mean rejecting a whole load of male patriarchal theology.
I have no such insight into Islam, but I would venture to think that this situation is equally possible. For that reason I don't think that it is necessary to be an atheist to be feminist.
Finally I think that the comparison between religious attire and stripping and prostitution is not valid. It's the difference between clothes and behaviour again. I think it is important not to mix the two.