Yo lo traduciría como "alianzas entre gays y heteros", para mantener el registro utilizado en inglés.

Un saludo.

Good luck!

More context is needed. The word alliance means alianza, which may be an indication that those clubs admit both gays and heterosexuals in their membership. In that case, you'll need to express that 'la organización o club admite tanto homosexuales como heterosexuales'. However, in the second line, you state that some schools admit homo clubs. In that, case, the statement should be interpreted in the sense that schools tolerate homosexual organizations or clubs, which may be stated as "algunas escuelas en los Estados Unidos permiten la proliferación de clubes de homosexuales". It's up to you to decide the context. Good Luck!

I know a good bit about this; my daughter and a friend of hers fought hard to have the right to organize a chapter of the GSA (this is a formal title, and there are many chapters of this organization in the USA. She and her friend were written up in Newsweek in the Mar. 20 issue.
There is a BIG difference between a "homo club" (this sounds rather derogatory to me) and a GSA. GSA's, by definition, welcome everyone with enthusiasm. They are not "sex clubs" but rather organization which offer support, information, and opportunities to make friends with people of many different orientations.