Lets say you are hiring people to work at a job that requires some sort of intellect, not just manual capacity. (For instance architect or music teacher).
You have two candidates about equally qualified, but you know that one genuinely believes that lizard-folk run the whitehouse and that Obama is literally a reptile using magic to look human.
Is it wrong to hire the other candidate on the basis that if this one can be so illogical on one topic that he might have other beliefs that might badly influence his work?
I think it is wrong from a legal standpoint.
However, as someone hiring, the person mentioning that he/she believes Lizard People rule the world is not only a bizarre belief, but a bizarre thing to mention in a job interview, because you want to come off presenting yourself as an intelligent, reliable, ambitious, approachable and eager employee who will be an asset to the company.
I teach English, and I have some controversial beliefs. I believe that we have been contacted and are being contacted by beings either from another planet or another plane. I believe that there is definitely a spirit world that exists, though I can't prove it. I believe in the concept of the 3rd Eye, and often see people inside my head with my 3rd eye quite differently. Often, I sense people's energy, their true self, and am usually right. I believe that positive thought actually has an effect on the physical world and other people, as does negative thought. I believe that all people will one day return to God, because I trust in the power of God and love. I believe that karma is like the law of physics - when we put out good, good comes back to us, and when we put out negativity, it also comes back to us, and each returns 3 fold.
I would never mention this during a job interview to teach.
I do have some controversial beliefs that relate to teaching:
If you treat students like children, they will behave that way.
If you treat adult students like adults, they will act like adults, and take responsibility for their actions.
I don't nag students to do assignments when they say they don't want to do them. I simply tell them that they don't "have to" do anything. They make a choice. If they choose not to do a presentation, it's actually easier for me. I just give them a zero. However, every action has a consequence, so they must choose the outcome they want.
I tell students to celebrate every mistake, because they have just discovered an error, which makes them learn, and prevent making it again. They become better speakers of the language.
Unlike many of the teachers, I have no problem with a student leaving to make a phone call, leaving to text, or leaving to go to the washroom. They are adults. However, I am not going to repeat myself when they return.
These are the kinds of things that I would mention in an interview.
I would probably not hire the person that believes in the Lizard People, a conspiracy theory that I personally find fascinating, mostly because bringing that up would make me see the person as kind of a freak in presenting themselves at the interview, and probably being kind of a Dwight Shrewt to have on the team.