I think it is a little more complicated, and probably needs to be done, at least in part, on a case by case basis, because few religious groups are truly monolithic in their beliefs, and that includes how they treat members of other faiths. A good example might be to compare JFK, who put his constitutional responsibilities ahead of any demands of his church, with Rick Santorum, who said JFK's comments separating church and state made him want to vomit. Any member of any faith who feels justified in using the government to enforce the rules of his faith on the unwilling would be disqualified in my mind from holding power. Would you say that his religious affiliation is the same as Kennedy's, its just his beliefs which are different?
Another couple of examples include the many churches in the southern US which not only endorsed and supported the Jim Crow laws (& earlier slavery) but also enforced them in the church. The Latter Day Saints were likewise pretty late to the civil rights party.