I don't really see neutral pronouns they/their being vastly problematic when trying debate something where nuance is everything to avoid your point being misunderstood.
Actually we lose a great deal when we lose the ability to call men, especially those who are enacting sexism, 'he' and 'him'.
They/them/their literally neutralises the sexed power relations at play in this fight. It obscures the fact that this is about male dominance, male power. Conversely, using male pronouns boldly - shockingly - draws attention to those power relations. It's like black light for the true sexual politics of the trans movement, instantly revealing its extreme misogyny. Highlighting that what's going on here is the same old male domination of women in postmodern guise.
Language mediates reality. That's why TRAs are so fanatical about enforcing their Newspeak. If pronouns were really no big deal, trans activists wouldn't be so obsessed with policing everyone's use of them. Pronouns are not merely a matter of 'courtesy', or an insignificant side issue. Pronouns are the whole ball game. Again, trans activists understand this. If they didn't, they wouldn't care so much about them.
I understand that under Mumsnet's new regime, we are forbidden to refer to men as 'he' and 'him' if men say that they are offended by it. I'm not here to argue that we should all do that anyway and risk being banned and/or losing the forum. I understand the necessity of pragmatism.
But I do want to point out that this submission to male authority over language costs us. It costs us the freedom to accurately describe reality, including the reality of what men do to women.