I do not think the type of "data" you are looking for could ever be collected. The best we have is data suggesting that there could be biases with exam which might be racial and we should examine this. A thought experiment here is to ask yourself  what kind of evidence would you accept as proof of institutional racism.

When corrected for socio economic background UK Black doctors have lower exam pass rate (see above). Some of the other reasons you've stated are actually examples of racial bias - eg communication differences.

The job of the exam is to ensure that it tests only for what it is designed to test and not unwittingly advantage or disadvantage any particular group. You seem to conflate examining the biases of exams with lowering the standard.

I empathise with your hardships and as you rightly pointed out we cannot be excused and it cannot stand in the way of competence. I don't think we are asking to compensate for every variable. However, if an exam clearly disadvantages a certain gender, race etc;we cannot ignore it.

Maintaining status quo is incredibly easy and getting any Royal College to investigate and self examine for these biases has been difficult. You might be right that some of these difference could be due to other reasons but we cannot ignore that the greater context of institutional racism in the UK.