Theoretically, no
gay Republican politicians exist because the GOP is a pro-"family values",
christianist party which despises LGBT people.
In reality, about 45.3412% of male Republican politicians (and climbing) rilly want some of that
viking love but act like homophobic dicks in public in a desperate attempt to hide their secret attractions. 'Til they get caught in a "compromising position", that is.
"_I am not gay!_" -- protest of self-identified not-gay
gay Republican IN state senator Phil Hinkle, who attempted to have a
business sexual relationship with a young man Hinkle contacted on craigslist. Hinkle was subsequently outed to his wife by the other man after Hinkle gave the man his smartphone in a state of panic. (2011)
See also: Larry Craig,
Tom Foley, Troy King, Roy Ashburn, etc. urban dictionary could have a spin-off site with just gay Republican follies.