Bad strategy.... better to use the diversity of gays and lesbians to unite the other factions. For example there are many more macho latinos who hide their sexuality than the latino drag queens. 

By breaking down sexuality barriers we would also be breaking down religious, economic, racial and ethnic barriers. Think Martin Luther King, Jr but even bigger. 

We should all participate in each others pride parades. This moral consideration goes beyond politics. Even the gay Republican caucus, the Log Cabin Republicans whose hero is Abraham Lincoln, have marched in gay pride parades.