"Bible thumpers" don't want genital checks either. Nobody does (except maybe troons) because it isn't necessary. It's blatantly obvious who belongs where. All anyone wants is to be able to enforce that like we used to- which didn't involve pants checks.
(And they usually come back with some one in a million story of a butch lesbian being "sirred" and kicked out of a ladies' room. But those cases bring up more questions. It takes a lot of work to look male enough to "pass" for someone who doesn't belong in the ladies'. Were these women just innocent victims, or were they trying to pull something over, too?)