It's important to stress that, while non-crime hate incidents *can* appear on an enhanced DBS, this is far from automatic:
"If an enhanced DBS check is carried out, which is limited to a list of high-risk positions like teachers and carers, it will not show up unless it is relevant to the job and is approved by a chief officer, who must consider an individual’s human rights of privacy and freedom of speech.
Under separate Home Office rules, chief officers must also consider allowing someone the opportunity to reply before information is disclosed, and it should not be disclosed if it is trivial, simply demonstrates poor behaviour or relates merely to an individual’s lifestyle."
Maybe even that's not enough to placate NJ's concerns. But if someone has a track record of being quick to demonstrate prejudice, or just generally being rude to their friends and colleagues and anybody who is different, it is probably relevant to an application to jobs where they are in a position of authority or power over others.
https://www.college.police.uk/article/police-hate-crime-guidance-court-of-appeal