why is it relevant?
I think it's relevant because one of the points of discussion seems to be about courts interpreting legislation and facts. In the case of the cake it is an interpretation of what does and does not constitute a request for a political message, as that is not a protected characteristic. Interpretations are influenced by assumptions that are made by the person or people deciding the case. As was seen in the Ashers case, different judges reach opposing conclusions based on their differing interpretation of legislation.
I was broadening out the discussion to suggest that assumptions made in interpretation of legislation and facts in court cases can result in conflict in society, in employment or in provision of goods and services. This can lead to an erosion of trust in the judicial system. I don't know if there is evidence to justify that perception of the judicial system, hence I was hoping that by bringing it up it was possible that other posters can link to stats or evidence on the judicial system discriminating in deciding cases that hinge on the perception of credibility of the respective parties.
For example in civil cases assumptions may have been made by a claimant that the respondent is prejudiced and discriminated against them based on a protected characteristic.
Or assumptions may be made in tribunals and courts that the claimant is dishonest or that the respondent could not possibly be a bigot, because finding for the person claiming discrimination would potentially destroy the reputation of the respondent. In criminal cases assumptions might be made based on sex, e.g. results in the court finding that an alleged criminal act was wholly out of character for the defendant.
It would be useful to see a study on outcomes of different types of discrimination cases and any investigation into why they might have been decided the way they were. You might consider that as irrelevant and uninteresting and I might consider your opinion on the matter irrelevant and uninteresting. Oh well.