Datun
Legally? Difficult to say. There's next to no case law to work with on this so trying to work out what's considered legal or not by the courts, which is why you can end up with so much conflicting advice coming from different legal experts. Essentially, what they are doing is trying to work out which way a court will rule based on already established constitutional principles that the courts use to interpret legislation, a rough handful of which are:
• What isn't forbidden is allowed - one of the fundamental underpinning constitutional principles guiding all law and how it is to be interpreted in England & Wales (E&W)
• Intent - What is the law intended to do? First preference tends to be given to any intent worded in the statute, followed by intent expressed by the Government of the day and/or Parliament & Committee that passed the statute, followed by guidelines issued by any Government as to how the law is to be interpreted.
• the Golden Rule - the act of interpreting legislation by not applying the literal meaning of the words laid down in statute where applying a literal interpretation would lead to '...any manifest absurdity or repugnance...', or '... obnoxious to principles of public policy', or where the wording the statute itself is ambiguous or it's literal interpretation would be absurd.
• Constitution and rights - we've got about 900 years of constitutional law to draw upon and the reason why society and the law isn't riddled with competing rights is because courts tend to actively rule in ways to avoid there being a conflict in rights.
• Lessons 2 and 3 when you first start being trained in Law, or study Law - Lesson 3 - the Law is not about Right & Wrong. Lesson 2 - the Law is not about Justice, or getting justice. Ideally, the Law is there to ensure the order and smooth working of society; more pessimistically it's a tool to ensure that those in power stay in power by attempting to enforce an ordered society. As a country we're an example of the former, places like Saudi Arabia or Uzbekistan are examples of the latter.
Now I'll try and keep this next bit as short as possible, so it will skip stuff, but the alternative is a truly massive wall of text, and it could still be that, so I apologise.
I'll cover the big elephant in the room first. Sex. How is somebody's sex defined in law. In terms of statute, there isn't really any big overarching statute that defines this is woman, this is man because there didn't need to be until very recently. Used to be the courts just went off of what was based on whatever government issued ID you had, which in turn would, somewhere along the line, be based on your birth certificate. Now, Government has issued directives and guidelines to the government departments responsible for issuing ID allowing somebody to have ID issued in one gender, whilst their BMD (birth, marriage, death certificates) have them listed as another. Whether you agree with the policy or not, it's a legal reality. So how will the courts rule on what determines a person's sex? One side will argue that birth certificates are the best determinator. The other side will argue that this interpretation and application of law goes against the aggregate wording and intent of the GRA2004, the wording and intent of EA2010 with special notice being given to how the intent of EA2010 alters the intent of GRA2004, and that this change of intent is reinforced by the issued guidelines to HM Passport Office et al; and that self-identification of sex is not forbidden in law, so therefore to avoid a ruling that is obnoxious to principles of public policy as laid out by successive Governments the Court should determine that a person's sex is the sex that they declare themselves to be, as long it is reasonable and not forbidden by law. Really difficult to see how that would end up. It's a coin toss to be honest, and I doubt that would see a court make a ruling so sweeping that it incorporates this much below the level of the Supreme Court.
Then there's the argument about how gender and sex are different things. Legally they aren't unless otherwise specified in a specific piece of legislation. The courts will recognise that generally the words are used interchangeably, both on a casual level of conversation, and within statutory legislation (GRA2004 s9.ss1 as one example).
Could a party allow a selection process that discriminates in favour of more than one protected characteristic? Theoretically, yes. It's not forbidden anywhere in EA2010 s104 so the first point on the bullet list would apply, but how would it apply if one of the characteristics is sex? Take a hypothetical Women's Party that has two selection processes: one selection process for all women, one selection process for BaME women. Would that second list be legal? Is it legal to incorporate two protected characteristics into a selection process (almost certainly yes), does the fact that the selection process incorporate the protected characteristic of sex mean that the selection process is covered by EQ2010 s104.ss7 thereby meaning that although the selection process discriminates in favour of BaME Women the overarching consideration is that the discrimination is based first on sex, and secondary consideration is then given to race (I'd lean towards the courts ruling yes, given the intent of the law), and if not, does the fact that the party offers a selection process separate from the BaME Women's selection process fill the legal requirement of EQ2010 s104.ss6 even though that separate selection process itself is only legal under EQ2010 s104 as a whole (perhaps).
So, to finally answer your question. When it comes down to an actual court decision, and I need to emphasise that, a court decision not a decision of another body, would a court rule that a woman who is eligible to be part of a sex-selective selection arrangement be discriminated against if such an arrangement included trans women for consideration in that selection arrangement. I don't know. Experience tells me that in cases exploring areas of law that haven't really been explored courts in the first instance really like to make their rulings as narrow as possible, so if I went with my gut I feel that that the courts will kick this decision back to whichever political party that's being sued, stating that it's up to the political party to determine who meets the eligibility requirements for a specific selection process, provided those requirements are reasonable in law. It doesn't look like a narrow decision on the surface, but it really is. With that decision the courts will have managed to avoid defining in law how you define somebody's gender since the new Government guidelines have come out, they'll have avoided producing a ruling that might have created competing rights, and they've avoided a ruling on the legality of self-id of gender. Otherwise, could a political party create a selection process that discriminates in favour for those who meet the qualifying conditions of the protected characteristic of gender reassignment? Certainly, yes.