You seem to be mixing up whether courts uphold unjustified perceptions, which you admit you have no evidence for, and some vague talk about people's perceptions. In addition what the sentences are for violence seems irrelevant to the question of discrimination in cases such as the gay cake by suppliers.
Yes because I decided to broaden out the discussion - if no one else is interested in broadening out the discussion they are free to not engage with my post. I don't have evidence, but by mentioning the issue I am opening up the possibility that someone else on this forum knows and more importantly has the time to find some stats on it, if they exist.
Even if the courts do not uphold the unjustified perceptions, if the CPS decide to prosecute someone for a hate crime based on unjustified perceptions or because they have targets to meet, it unfairly penalises a defendant who will have expensive legal fees to pay. The common theme is badly drafted legislation and a judicial system or CPS with an agenda that might lead to having to defend yourself against unjustified accusations of discrimination.
The Equality Act reverses the burden of proof in all cases except those which relate to a criminal offence. Sections 136 (2) and (3) provides that if there are facts from which the court could decide, in the absence of any other explanation, that a person (A) contravened the provision concerned, the court must hold that the contravention ocurred unless A can show otherwise.
Where the allegation concerns a criminal offence the criminal burden of proof (beyond reasonable doubt) applies.
https://www.lawsociety.org.uk/support-services/advice/practice-notes/equality-act-2010/