It shouldn't be a matter of the faith they claim to follow, but their ability to do the job . Sometimes all a faith does is give a person a few rules as to how to live in a modest, and decent manner, it's only when they drift into fundamentalism there tends to be a problem. I don't think anyone has a problem with live modestly, care for those in need, respect marriage/ your elders/ your family. That seems to be at the core of most beliefs and also at the core of many peoples moral compass. Religions were created to moderate,and control people's behaviour, it's not surprising they have values in common. Even dietary rules arose from the need to avoid food that was potentially harmful in a middle East pre refrigeration and safe husbandry practice.
Maybe we should make less of religion and more of character, intellect and ability