Everyone on here is entitled to their opinion about whether being "out" on your application will harm an applicant's chances or not. I just thought I would chime in with what I have been telling others in the past.
Discussing LGBT advocacy extracurriculars are great, especially since it shows your devotion to a group of that may not get medical treatment the same way heterosexuals do. However, it CAN cause problems with your application. If your application were to be read by a conservative or homophobe, you're toast. Granted, that is not how it should be, but they'll just start finding reasons...
Unfortunately, this discrimination should not be there, but it is and I'm not necessarily sure you want to run the risk of having that "bring your application down". I've given thought to discussing this "adversity" and whatnot in my own application, but I decided against it only because of the hard stuff that can rise out of talking about homosexuality and its difficulties on paper.