Seriously, people like that manager ARE that stupid. I say this having worked in retail, social services and marketing. I have seen things from people, heard things from people, that you would never in a million years imagine someone was stupid enough to say on a recorded line. And it wasn't just the ordinary folk but professionals as well.

In many places, checking a different gender from the one you are legally assigned can be consider "lying" on your work application and be grounds for rejection.