http://www.foxnews.com/us/2014/08/02/emerging-muslim-movement-embraces-gay-and-interfaith-marriages-female-imams-and/LOS ANGELES – Omar Akersim prays regularly and observes the dawn-to-dusk Ramadan fast. He is also openly gay.
Akersim, 26, is part of a small but growing number of American Muslims challenging the long-standing interpretations of Islam that defined their parents' world. They believe that one can be gay and Muslim; that the sexes can pray shoulder-to-shoulder; that females can preach and that Muslim women can marry outside the faith — and they point to Quran passages to back them up.
More, from 2012:
http://www.huffingtonpost.com/2012/03/29/progressive-muslims-launch-gay-friendly-women-led-mosques_n_1368460.html
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Site:

http://mpvusa.org/Muslims for Progressive Values (MPV) is an inclusive community rooted in the traditional Qur'anic ideals of human dignity and social justice. We welcome all who are interested in discussing, promoting and working for the implementation of progressive values - human rights, freedom of expression, and separation of church and state - as well as inclusive and tolerant understandings of Islam.