Many Islamic authorities claim that homosexuality is categorically forbidden, but the reality is much less clear-cut. There are no verses in the Qur'an that unambiguously condemn homosexuals, and there are some that suggest they can be tolerated in Muslim communities. In addition, reports from Hadith that condemn homosexual and transgender persons are of dubious authenticity. Islamic law itself does not speak about the issue of sexual orientation, but speaks about sexual behavior. The interpretation of different sexual behaviours in Islam is beginning. The first Muslim to publish widely on issues of sexuality and Islam is Scott Siraj al-Haqq Kugle. His book "Homosexuality in Islam" was published in 2011.
In many Muslim lands persecution is still rife - read an excellent article about this in the Economist here (from 4th February, 2012).
In the database, you can find several discussion papers and reports on issues of Islam and LGBT people. You can also find more information on the following websites:
Inner Circle based in South Africa, the largest formal organization for Muslims who are queer in the world.
The Safra Project is a resource project working on issues relating to lesbian, bisexual and/or transgender women who identify as Muslim religiously and/or culturally (Muslim LBT women). Amongst other things, the website contains a very elaborate bibliography on sexuality, gender and islam.