Yes posie, muslim women do use this term, and yes they use it to separate muslim women from non muslim women.
But they don't own the word. And IME many of the ones I met weren't overly sisterly either.. unless trying to shag one's other half is a sisterly right 
(ew)
When younger, I have to say, that due to the cruelty suffered at the hands of female colleagues at school, at work etc, I was not overly bothered to have female friendships. It was all too much effort, the she said, she said stuff, cosmetics and boys/men, all of it left me cool at best.
since becoming a mum, and living in a male dominated islamic society, I tell you I couldn't have any less interest in the male of the species if I tried.
Living under that regime, I grew to truly appreciate the efforts and struggles fought on my behalf over the years so that I have a say in politics, in law and in work. Women and men laid down their lives and reputations so that I can live as I do today in this glorious country. Where a woman CAN be all she wants to be, as demanding a job as it is, at least she has a choice.
Patriarchy is a classic proof of the phrase, Power Corrupts, and Absolute Power Corrupts Absolutely. There HAS to be balance, and by the female of the species carping and bitching at her fellow woman, we are going to find it very hard to be taken as seriously as we ought to be.
We have to stop this objectification of women, we have to rebuild female esteem to expect and demand more, to value ourselves and each other more.