Gotta say, I think you should mention it if you want! I visited here and they seem to be actively trying to increase diversity in all forms. There's an LGBTQ student group, and the multicultural center is new, but driven. I don't imagine that you would be discriminated against by Tulane admissions. On the contrary, I think it could be helpful. Of course, if you don't think its important to your identity, leave it out if you wish. But I don't think you should omit something you might otherwise mention for fear of unfair treatment, at least at Tulane. They just want to know who you are and what makes you you!
