I’m a Samaritan and either your training was terrible or you misunderstood. We can rarely transfer callers, because of practical reasons about the set-ups of our rooms, but we would never ever insist on a female caller being moved to a man. And we are also explicitly told to never move a man to a female Samaritan, because why would a male caller need that (unless for sexual, and thus call-ending, reasons)?
Likewise, we don’t even ask the sex of a caller, let alone pronouns.
Again, I’m not sure if you had terrible training, but this sounds a bit like a conscious and untrue slur. (Really fucking hate Samaritans’ social media posturing and lying around trans stuff, though. I console myself that the vast majority of callers don’t ever talk about those issues though, and we’re there for them.)