Nobody ever said there is a blanket ban for trans people, or any other protected characteristic under the EA. It remains that in limited circumstances exclusion is lawful. You've consistently presented this as not being the case in order to confuse readers and make them think men cannot be excluded from women's single sex spaces even when that exclusion is proportionate and legitimate (as can other groups in certain circumstances). The EQ advice goes into several examples in order to make this clear.
Fortunately people on here aren't stupid and they know that a gay men's choir can legitimately in law exclude both women and straight people and that Usain Bolt can't run in the Paraolympics.
You're certain on that point, no need for you to a quick search of your own posts?
It's a guide for employers and service providers. The case by case aspect is the scenario put forth by the employer or service provider, not that service users have to be assessed on an individual case by case basis. Ikea can think about the scenario of who they want to use their ball pool, decide it's under 10's and legally exclude over those over 10. They don't have to admit small 12 year olds or baby faced adults. And if an over 10 sneaks in they can ask them to leave. All permissible under the EA.
For the millionth time.... nobody is excluded for being trans. They can be lawfully excluded for being male or female from spaces and services intended for the other sex. When proportionate and legimate etc etc etc....
This is the confusion and obfuscation that you endlessly promote. Nobody is banned for being transgender. Not from sports, not from jails, not from refuges, not from apps, not from changing rooms.
ALL such judgements have to be made on an individual basis. Otherwise how is anyone going to know that they are breaking the Equalities Act?
Ike may well have carried out a risk assessment for using their ball pools, and decided that because of a number of factors, often weight is the most important consideration, and they have used the average age of a 10 year old as the cut off. This is an attempt at "being diplomatic" as they can ask the age of the child a lot more freely than they can the weight. Check the age weight requirements for any toy or sporting equipment the next time you go near any. It's not there for your safety, but for manufacturers to point out to you when you complain that something designed for a ten year old broke when you used it.
Theme park/fairgrounds operate an individual assessment for people who seek to go on some of their rides. At times it's age restricted, at others it's height restricted, Not as high as this line being a common one that most pass unnoticed, unless you happen to be waiting in line.
All done on an individual basis.