Nobody is being banned for being trans. Males can be excluded when appropriate and justified, regardless of how they identify. It doesn't have to be on a personal case by case basis, it can be all males. Several sports organisations seem confident enough to enforce a protected category for females - ie a blanket ban of males - so I look forward to the legal challenges that bring up these court tested legal precedents of which you speak.
Earlier in this thread you were talking about women's toilets and used the phrase 'that's why we exclude them'. You were speaking as if women had the legal authority to exclude trans women from women's toilets. You were challenged for it.
The terms of the availability of the exclusions is set out with the legal acts. You are incorrect in your reading of case-by-case basis. For example, with regard to prisons, the law sets out that prisoners are risk assessed on a case-by-case basis. There is no blanket ban on trans women being in women's prisons in the UK, precisely because the legal precedent has been set by the courts. Now you will argue that legal precedents can be overturned, which of course it correct. However the precedent remains the precedent until such time as it is superseded. At this point in time, I am not aware that a change to that particular legal precedent has occurred, therefore as far as I'm aware there can be no blanket ban.
The inclusion or exclusion of trans people from sports is again set out in the act. Sporting bodies can exclude trans people from certain sports, however they have to show that they can justify it. It's unlikely that chess could be a justifiable exemption, but hurdling might well be.
We both know this is a complex area, one where there has been insufficient research, and where there are no simple answers. I have offered one opinion on this previously as a possible step to a solution.
As far as toilets and changing rooms are concerned, the law sets out that proven intent to cause alarm or distress can be dealt with under the law, but excluding people with no previous history of intending alarm or distress is not a proportionate means of meeting an end.
And here it is again, there is nothing in law that says that a woman or a girl must be protected from seeing a naked male body regardless of how they identify. You may not like that, but that is the way the law stands.
By the way, I've given you the links before with regard to the legal precedents, but you simply brush past them as not relevant.