Well, I need to first issue this qualification: Before I look at a candidate's "denominational ID," I look at their spiritual fruit. Example: 1992 candidate Clinton & 2007 candidate Huckabee are/were both Baptists (Clintons are now Methodists, or at least, Hillary is)...but I don't see them in the same light...(and I think many here would agree).
So, after I look at social issue positions & voting record & electability (among other issues) I zoom in on spiritual fruit & character, which includes their other-worldly commitments. (You can't separate their other-worldly commitments from their character).
Now, those "faith" IDs that would not cause a trigger concern issue for me would be any of the historic Christian faiths (Protestant; Roman Catholic; Eastern Orthodox) or a Jewish candidate who calls upon the God of Abraham, Isaac and Jacob. There, I guess that represents the faiths of about 86% of Americans...and I daresay the number of Congressmen who are likewise linked to said affiliations is probably over 90 percent.
Yep, and look what we have. I think your idea of looking at past performance rather than the faith label is a good one. Faith labels often don't tell us much, as you pointed out.