The "pushback" is all noise and no substance. The Scottish Government accepted the ruling, the UK government accepted the ruling. The Attorney General is pro-sex based rights and is making sure that the ruling is complied with top down. The EHRC are doing the same.
The FA, the SFA, Cricket, Netball, Pool and other sports associations are reverting to female-only rules. The British Transport Police has done the same. Slowly most organisations that are accountable to government and have insurance policies that require compliance will make the change. Some will resist because they will argue they don't have to provide a 'single sex' only service (Ladies Pond for example). These will probably need test cases.
All of the businesses I have seen sending 'supportive messages' to their 'trans, intersex, non-binary colleagues' (I swear they get AI to write these) are completely lacking in any action or substance. They are generic, non committal messages along the lines of 'always support trans people' and 'stand by them' - they know they cannot say they will break the law.
As for the BMA - it's a trade union - it is not the NHS and it is not a Royal College. It's just there to collectively bargain wages and working conditions.
The ones opposing it are making the loudest noise: TRAs peeing in public in Parliament Square, mid-ranking celebrities (face it, when Eddie Redmayne - someone who can barely open a film on his own - is the biggest name you can muster, it's not 'A-list'); a tax lawyer with a grift, a clear mental health crisis and a track record of failure and some Guardian journalists.
If celebrities are comparing their Trans Rights stance to the MeToo / TimesUp moment then we can all sleep easy at night, as that movement was a failure which changed nothing and achieved nothing. It did sell a few badges and get a few lower level actors noticed though - so there's that.
The interesting thing about the celebrity letter was how it called on a lot of publicly funded or owned bodies like the BFI, BBC, Channel 4, Arts Council to support trans rights. These organisations will be in a quandary - when government funds are being cut left, right and centre, especially for anything discretionary - do they really want to start a fight with the people that pay them? I have worked in both fund-raising and the independent film sector and complying with Equality Act is a central plank of securing grants. Lisa Nandy has already said she's not ruling out ending the licence fee. And Kneecap will be helpfully raising wider awareness of the risks arts funding bodies take when they make grants. The independent film and TV sectors in the UK cannot exist without government subsidy and visibly complying with EA2010 is a condition of that subsidy.
I think there are still risks and concerns - especially at lower level and in the NHS but the pushback at the moment is all noise.