I've done a little more research into Equal Ops law and have found lots of people claiming it is unlawful to discriminate on the grounds of "religion or belief". At first glance, it really might appear unlawful to discriminate against someone who believes that black is live and red is neutral (I know, EU rules require new colours these days, but the vast majority of houses still have red/black wiring for the bits the householder doesn't usually mess with).
So I checked out the relevant statutory instrument which seems to be The Employment Equality (Religion or Belief) Regulations 2003. Fortunately, "religion or belief" is quite specifically defined as:
"any religion, religious belief, or similar philosophical belief"
I doubt you'd consider black-is-live-red-is-neutral to be religious or philosophical, so I guess we're OK on that point.
However, the sincerely-held, but probably delusional, quasi-religious belief is going to be trickier. It really does seem to be unlawful to discrimate against an employee (or potential employee) who, say, sincerely believes something that would be harmful to our business (e.g. that nails and hammers should only be held with the right hand, thereby making it impossible to hold both the nail and hammer at the same time; or something far more serious like believing that members of another religion should be exterminated.)
I can't find an exception for this sort of thing. There is an exception to allow discrimination if it is in the interests of "national security" (reg 24); and a rather complicated exception about Sikhs, turbans, helmets and building sites (reg 26). There is also an exception (reg 7) if your business really needs to employ only people who are members of a particular religion (presumably to allow the Church of England to only employ Anglicans as vicars. It would be awkward if they had to also employ Catholics and Muslims), but it doesn't operate the other way. i.e. if you need people to be members of a particular religion, you can reject people who are not members of that religion. But we don't need people to be members of a particular religion, so we can't use that exception.
I suppose, though, that if the person's belief prevents them effectively doing their job (as with the hypothetical nail / hammer example), that's going to be the over-riding principle, right? So you are rejecting them because they can't do the job, not really because of their belief? Surely it's OK to do that?