I'm currently living in a Muslim majority country and while I totally agree we can accommodate them in western countries the sad reality is the vaaaaast majority of non western Muslims are going to quote the Quran about there being only male and female and the Arabic language reflects this as well since there is no neutral gender. I speak Arabic (not fluently but enough to understand my mother in law when she wants me to do stuff around the house and understand what my in laws are talking about) and this concept of third gender just...doesn't...render. I'm very impressed by American Muslims since theyre very accepting in general of LGBT stuff and do a bit better of a job at that than Christians in America. But I guarantee LGBT people here in the middle east suffer. About 30 percent or more of my friends here are queer and some of them fled their families in fear of being murdered. It is VERY difficult (please read this point and meditate on it) to manage respect for both Muslims and LGBT when those two identities often produce disastrous results when combined. Again, obviously I have Muslim friends here, some of whom don't personally care one way or another about the LGBT issue because they themselves are good people, but chalking up lack of LGBT rights here in the mideast and other Muslim majority states to anything other than the religion is deeply misguided. I'm not saying this to YOU specifically, I'm just saying you may have personally met very good people where you live who realize their status as a minority entails they must protect other minorities as well given their shared interests.