I thought red was considered the "power necktie" when you're trying to be all Alpha Male. In the 1920s, 30s and 40s ties were heavily decorated, though, so perhaps a solid red tie would have been the exception, I dunno. It had been my understanding that gay men back then would dress "foppy" (effeminate) with an overflowing handkerchief from their jacket breast pocket, with a red or white boutonniere, and a soft felt hat with a wider than average brim, often in a beige or other light color (all men wore hats outdoors with a jacket).
The Queers United site where the OP photo & quote originated describes itself as "The activist blog uniting the Lesbian, Gay, Bisexual, Transgender, Queer, Intersexual, Asexual community & Allies..." Think they left anybody out? I don't even know exactly what "intersexual" is, a word my spell checker doesn't recognize.