Two flaws immediately apparent in the above. One - there are plenty of religious people who think critically and historically many of our great thinkers have been actively religious. Isaac Newton was a deeply religious man, for example. Two - that's an appallingly inconsistent benchmark. By it, you would ban some person who prays regularly but makes all their economic policy decision based on evidence, whilst allowing in some dogmatic and committed marxist who disregarded all evidence in favour of ideology. As one example of how being religious is far, far from where you should start if you're going to start disqualifying people from public office.