So the trans male example is an interesting one. An argument can be made that this is discriminatory against trans men as it seeks to exclude them from selection. There's two problems with that:
i) The way the law works in England & Wales, and across Britain as a whole, means that a trans man would have to bring a case to court arguing this point. In terms of Equality law courts do not work on hypothetical situations, they need an actual case in front of them. Not only that, but plaintiff also has to actively show that they have been unreasonably disadvantaged, to the point of being discriminated against, under the terms of EA2010.
ii) Labour has two lines to argue with the court;
a) this is solely an internal political party issue as to how, within reasonable limits, they choose to define whether somebody meets the criteria for selection or not and that is solely an internal party issue to define, again within reason, what those criteria are. Therefore, whilst it would be unreasonable to say that women may not stand for selection, it is reasonable for the Labour party, via it's own internal mechanisms, to define, again within an objective test of what is reasonable compared to what the goals are, who is a woman for the purposes of selection to a specialised short-list, and that if a person does not meet that criteria, they then have the full opportunity afforded to any party member to join a general short-list, and therefore are not being unduly discriminated against. This line of argument has a fair degree of success. Courts are loath to get involved in internal political party issues and unless the plaintiff can show that the Labour Party is acting objectively unreasonably in their particular case by not accepting that they are woman even though they personally identify as a man (and that's a really tricky proposition), the courts will probably accept the argument that the specialised short-list has been solely drawn up under the provisions of EA2010 s11 & s104, and so s7 doesn't come into play.
or b) if the courts decide that the Labour party has been too broad in its internal definition of who is a woman solely in terms of use of definition within the internal workings of the party (and I should point out that is really unlikely, these are definitions in use for internal party business only and have been decided for use either directly by party members through conference measures, or through decisions made by party officials who themselves are party members duly elected into position to make those decisions by party members), then the argument can then be advanced that although the specialised short-lists in question are being drawn up under the auspices of EA2010 s11 & s104, with some level of regard to s7, the trans man in question is not being unduly discriminated against as the discrimination being imposed is of less harm than the benefits being accrued by providing a certain level of discrimination, and that mitigation of that discrimination has been provided through relief as the plaintiff still has full access to all other applicable short-lists. The second part of this argument is less certain to succeed, because it comes down to asking the courts to balance perceived harm against the benefits of achieving a beneficial goal.
Somebody asked about discrimination against agender, or non-binary, people. Again, part (i) of the above argument stands, somebody who is agender or non-binary would have to bring a case, and then the courts would just bounce the case, claiming that it's internal party issue because at the moment neither Westminster, or the relevant national ruling bodies, recognise the existence of agender or non-binary people and therefore the courts cannot make a ruling because these aren't recognised characteristics within law and aren't covered by EA2010. It is solely up to the internal mechanisms and workings of a political party as to how, if, and when they choose to recognise and make provision for agender or non-binary people.
If I remember right, somebody asked about the use of the term 'self-definition' or 'self-defining'. Trying to make that an issue in court is a no-flyer. A really quick legal argument off the top of my head (so not the best) that could be placed in front of the courts would look something like:
i) {Objective test for reasonableness) It is reasonable to make the assumption that within an average person's lifetime they will have, at some point, filled in a field or ticked a box on a form that asks for their sex or gender, and that
ii) unless specifically stated otherwise within the body of law, the law recognises that the use of the terms gender and sex are used interchangeably within common use, and that
iii) given the provisions of (i) and (ii) it is reasonable to assume that an average person will have self-defined their gender and sex via self-declaration.
I should point out as well, these are just personal observations of how legal arguments may be made. There are going solicitors and barristers involved with a great deal more experience who are going to be much more sophisticated and nuanced arguments so please take what I'm saying as solely a personal view on the legal side of what arguments may be presented.