Tisei, a former state senator and his party’s 2010 nominee for lieutenant governor, said that if any one of them “is able to break through the barrier to talk about LGBT [lesbian, gay, bisexual and transgender] issues as a Republican,” it would be damaging to the Democratic Party as a whole.

DeMaio, a former San Diego city councilman running in a highly competitive race against freshman Rep. Scott Peters (D-Calif.), echoed Tisei.

“LGBT progressive Democrats don’t want the Republican Party to change,” he told The Hill in an interview. “They want it to remain the boogeyman” and blame the GOP when progress isn’t made on social issues.

Some LGBT activist groups, including the Gay and Lesbian Victory Fund, have not welcomed DeMaio with open arms during his political career.