So if a forty year old white, straight male who identifies as male wants to join a pony club for girls of 10-14 and he's told no, on account of being a forty year old man, that's two of his 5 protected characteristics (race, age, sex, sexuality, gender identity) used as a reason to exclude him. (Race and age.)
You are saying anyone can be excluded or refused service from any private business or establishment for any reason at all, except if they are being excluded specifically because of a protected characteristic.
If all protected characteristics are equal in law as you say, and the only difference is that some demographics with certain characteristics are more likely to be discriminated against than others, then I guess he's joining the pony club if he wants to and he'll go to court to fight anyone who says otherwise and he'll win.