Do oddball beliefs disqualify you from certain jobs?

It has been suggested by the more militant opponents of ID that people who believe in ID or other non-naturalistic worldviews should be disqualified from teaching, or from receiving Ph.D.s, or from having columns in Scientific American, amongst other things. I was interested to read what Robert Lacey wrote about the organisation that supported "The Few" in the Battle of Britain.

This formidably efficient back-up organisation, unparalleled in aerial warfare to that point, was the work of Air Marshal Sir Hugh Dowding, a cagey character generally disliked by his fellow airmen, who nicknamed him 'Stuffy'. In fact, 'Stuffy' had some most original and unstuffy personal interests that included theosophy and a belief in fairies, angels, flying saucers and the possibility of intelligent communication between the living and the dead.

"Great Tales from English History", vol.3 p.251

What impact did this collection of odd beliefs have on Dowding's ability to do his job? Apparently, none at all. He had a clear idea of what he had to do. He had two main principles - firstly that technical superiority should be the priority, and secondly that expensive machines and the lives of trained airmen should not be risked unnecessarily. The British victory in the Battle of Britain was the first occasion when Hitler was defeated, and it seems in part to have been down to Dowding's leadership.