Hello OP!
I was a senior hr player but have taken a couple of years out to be sahm and am itching to get back into HR.
I keep thinking the same as you.
I think critical conversations might be what you need?
My husband is a business person and across the office he heard an open conversation about some younger more woke staff about why they should have uni-sex toilets and he got stuck in with no way and look at what can go wrong and then it went into trans rights and he was gender critical. He didn't think much of it but said it was interesting how women around his age cane up to him quietly afterwards and told him thanks and they agree but they obviously didn't feel comfortable being vocal .. so he came home and told me about it and was surprised some women were reluctant to share their views.. but you see he is an independent business person and senior enough to say what he wants with very little consequence as he is more of an entrepreneur rather than employed.
But I think the key is quiet challenging conversations.
Find out what the bank spends with stonewall?
Who agrees it?
Who gets control of the budget for it?
Do they provide training ? Is it crap? Can you change training provider with something better without the political slant from stonewall?
Can you do some confidential surveys to canvass views?
Who manages the relationship with stonewall? Why, what does the bank think stonewall does for the bank?
Have conversations first and then start putting up alternatives?
It is so difficult isn't it? What really worries me from a hr perspective is data collection and just what a load of bull shit it will be if we collect information on variant gender which therefore muddling up relevant sex factors.
I also feel deeply uncomfortable with the whole pippa Bruce thing, I mean as a women am I meant to embrace a colleague if they cross dress ?? (and in my opinion play out a character which demeans and objectifies what it is to be a woman).