Yeah to a lot of this. I think I can spot the direct cause of so much of where his responses go off the rails of compassion: Pete loses the argument in the simplest way of letting the Republicans build the vocabulary here and just using their phrases verbatim. (It’s been how many decades since every liberal was asked to read “Don’t Think of a Pink Elephant” and we’re still falling for this?)

says something like “no boys in girls sports,” which is a phrase that they use

Yeah Pete, it’s a phrase they use because it heats up the game. It’s makes people angry about strawmen (almost literally). Just repeating it this way (and also it’s twice in the two quotes at the top here) is already a loss of compassion and “compromise” to the wrong side of the Overton Window.

The undercurrent here is nothing to do with boys wanting to play girl’s sports: it’s everything to do with girls having to prove they are “girl enough” to play girl’s sports.

Trans girls are girls. Full stop. Even implying that they are boys is failing to have compassion for them and their struggles. Letting them clutch pearls about “boys in girls sports” is letting them win against the battle of compassion and moving the frame of the discussion too much away from girls being forced to prove their “girlness” (and it hurts cis girls, too!), it’s a failure to protect real people’s daughters. It’s allowing them to move to a frame of protecting other more “virginal” or “virtuous” daughters from the fear, uncertainty, and doubt about boogeymen (literally) that almost entirely don’t exist. (And yes, protecting some of them for getting their feelings hurt by losing to athletes they personally don’t like and may be bigoted towards.)

It shouldn’t be a surprise that rephrasing tactic works and how fast it spreads in Republican media and social media. That’s more reason to fight it every time you hear it or at the very least don’t repeat it in their words because you’ve already lost, Pete! (Again we’ve known this playbook for too long and it’s infuriating how many easy wins they get that they should not be allowed.)