Should I mention controversial clubs/organizations on my application ?

If that's something that you're passionate about and schools don't want you because of it, then I think that you might want to reevaluate whether or not that's a school that you really want to go to. I think that schools would rather see that you stand up for what you believe in rather than trying to hide something to be more likable. Not everyone is going to have the same opinions on everything but as long as you can explain logically why you believe in the things that you do, I would hope at a professional level that people can appreciate a diversity of opinion.

Well, Let me say this. I would think that schools would be accepting of LGBT people. They should be pleased to see someone stepping up for what is right. There is a lot of discrimination against LGBT people currently, and this should serve as an example of an individual (you) who respects all human beings. I don't care if the school is conservative. They shouldn't be offended by this at all, and I want to commend you for your involvement in these organizations. I believe you should mention it, however if you're really not sure, then you could contact them.

I'm like 99% sure that theres some nationwide legislation that prevents schools from discriminating against the lgbt community. Three of my supplemental applications asked my sexual orientation, and there has to be some legal reason why they ask that. If you were passionate about the organization you should definitely put it on your application. Now, the personal beliefs of people on each school's admissions committee might differ, but it's still illegal to discriminate against the lgbt community. I also know a ton of conservatives who are pro-lgbt, so I wouldn't necessarily assume conservative schools = anti lgbt.