You seem to think no-one here isnt in a similar position.
There is an assumption that being here means you don't care about transpeople.
Recognising sex is real and can't be changed isn't ever an extreme position. It's the only possible position. It's the conclusion that the SC ultimately came to.
The trouble is this is at odds with the idea that doing so is bad, doesn't respect transpeople and harms them. And people like you are desperate not to hurt people they care about.
Unfortunately it's an unreality. You can't protect people from the unreality of their belief. This doesn't mean you can't protect them. It just means you can't protect them from the truth.
Indeed trans people NEED the definition of sex to mean sex. Without it, you can't identify someone trans from someone non trans. The whole point is that the status of being trans is in relation to your physical being and sex. If you can't identify sex, anyone can claim trans status. That's me, that's you. That's anyone who wants to get the legal protection of classing yourself as trans. Women lose their protections and homosexuals also lose their protection. Ironically you have to see sex to see transphobia, homophobia and sexism. This extends from safeguarding to sport to healthcare to education to workplace to everything.
You can't replace sex with gender because you still need to refer to reproduction and healthcare. These protections protect HCPs and transpeople alike. If you were forced to treat people as the gender you are in healthcare you would risk the health of a patient and a doctor would be potentially forced to harm a patient. Equally if a doctor refused to do this and treated a patient as the sex they are in a professional manner they would still risk being sued by vexatious nutters. This isn't okay in either scenario. Thus you have no option in law but to recognise this. In terms of patient care it also needs to be referenced whether a patient likes it or not. There are scenarios such as blood donation where this is particularly important not just to an individual but to others.
You also can't define gender in law easily. And certainly not without referencing sex. Otherwise you get bogged down in sexism. This is why everyone avoids the question. They know it's a circular argument that relies on sex as it's foundation.
Once you understand these points there's literally no where else to go with the argument. Sex isn't a biased anti-trans thing. It's a neutral identifier that is essential to women and transpeople regardless of how either feels about it. It has to be recognised in law.
From here the next most important thing in terms of law is safeguarding. That's a human right. Women, homosexuals and transpeople all need safeguarding - you can't safeguard lesbians without seeing sex and homosexuality. You can't allow transwomen to colonise the concept of lesbianism as that's homophobic. You can call yourself homogendered but not lesbian or homosexual. Otherwise you harm lesbians in law. You also have transpeople who are same sex attracted who still need the protection of being recognised as homosexual even if they wish to call themselves something else. This extends to human rights, equality considerations and to health and safety.
Transpeople need the protection of sex and gender reassignment (where applicable). Both rely on sex.
Then there's women who rely on sex and have a legal right to exemption and single sex on the grounds of legitimate aim. This is where transpeople get the hump - they fail to recognise the legitimacy of the legitimate aim. Instead they think they have the absolute right to inclusion. This isn't true. They have a right to fair treatment, privacy, dignity and protection. But not automatic inclusion on the basis of their gender identity or gender reassignment.
This is unavoidable due to the harms to women and discrimination against women. It just means transpeople need different provision. This is what isn't being accepted.
This isn't womens problem to resolve. Nor is it for them to compromise their rights. It's for rights for transpeople to be exercised in a different way which protects both parties.
There isn't a way around this. Too many transpeople don't want to acknowledge this. Nor do their allies who don't want their friends and family upset. But ultimately it's the only way they can be protected and other groups be protected. Because people are nice they don't want to admit this so go into a state of denial or even fence sitting flapping their arms that they think it's difficult and they don't want to hurt said persons feelings. The trouble is those feelings are based on an untruth that has no substance and definable qualities that the law can discern without harming another. There isn't an ability to uphold a fantasy in law as much as anyone might wish it. But no one wants to be the 'bad guy' and say this out loud. So they couch language and pretend it's harm. It's really not.
We have to recognise the transient nature of gender reassignment and gender incongruity - especially in child - because of irreversibly, various at risk groups (children, autism, trauma, abuse, homosexuality) because we also know about harms and we know about detransition. And various rates associated with this. We can't ignore this. Minors have a higher priority than adults in terms of human rights too. We do not have a choice if we are neutral about this.
It all comes back to a small group not liking this and every one else being fucking terrified of saying it or even thinking it.
So it can be resolved fairly and safely. If we acknowledge this is all as neutral as it is.
The problem is that we have so many people in denial or unprepared to say no where appropriate.
This isn't a law problem. Nor is it a GC critical problem. It's a problem with people tripping over themselves to be nice rather than understanding that it's not about being nice and that sometimes being nice isn't possible for reasons that actually protect an individual even if they don't wish to accept that.
The law and society can only reference material reality to offer protection and fairness. It can not prioritise belief over and above this because harms always gets precedence. There's some bits around the edges but ultimately if you have a group set up for women and the premise of the group is about how women face barriers to sport because of sex, it has to reflect that legitimate aim. You can't fudge it to be nice because you undermine the legitimate aim. This doesn't stop groups which might be inclusive of transpeople. It's just that the premise of that group has to be focused in a different manner.
Inclusivity is not a right on its own - that's the point.