I realise that you would rather obtain responses from Muslim correspondents, but I hope that my own experience will be helpful.
As a gay male, I have found that Muslims I have met are more interested in, than 'horrified' by, my lifestyle, and my choice to be open about it. It seems to really fascinate them that I have the choice to be open. Of course, the Muslim world is a big place. Those I know personally come from Iraq, Algeria and Egypt.
Another correspondent referred to geo-political issues as being a more consistent grievance, and I have found this to be true. It would seem, from my limited experience, that moral issues are more a religious-fundamentalist concern.