They can now. They couldn't up until 5 minutes ago, and trans identified men are still trying to overturn that ruling in court. It's also not permitted to refuse a trans midwife in the NHS for example.
Ok so take gender identity out of the equation if you must, I am sure many trans identified people would disagree with you that it's not a protected characteristic and we are certainly expected to behave as if it is. I couldn't sling someone out of my business establishment or refuse to deal with them purely because they were trans.
But the fact still remains, you said all protected characteristics were equal in law, it's just that some people face more discrimination than others. My example shows that while you may possibly be right in theory, in real life you are very wrong. No straight white male is getting any protection in law when anyone discriminates against his whiteness, his sexuality or his maleness. It happens daily in the name of DEI and it's totally legitimised.
The sort of invective regularly directed at straight white males with 'white male privilege' frequently verges on hate speech and would be considered hate speech if it were directed towards anyone with a protected characteristic that marks them out as a minority of some sort in this country. But it's tolerated, ignored and indeed encouraged to discriminate against white men and speak disparagingly of white men, and to hammer home negative stererotypes towards white men these days.
With the possible exception of trans identified males who might be turned down for a job or refused service for being trans, there is no protected characteristic in being male and white and straight, is there? But that brings me back to point A. Gender Identity as a PC.
Age isn't really a protected characteristic either. Again, it may be in theory but in practice there are far too many exceptions and caveats where it isn't, to the point that it's pretty useless claiming it as a protected characteristic for most people.
Don't get me wrong, I am not making a case for the poor, hard done by white man. I am just making the point that while in theory we may all have the PCs of age, sex and race, in reality that means absolutely nothing for a huge swathe of people.
Many people are allowed quite legitimately to be barred from certain positions, activities and events by people whose PCs apparently trump theirs, or by organisations that have a DEI policy that discriminates against certain demographics in the name of being a 'safe space' for other demographics, or for reasons of positive discrimination. The problem with positively discriminating for certain cohorts of people, is that you in order to do it you have to negatively discrimate against others, don't you?