Why does America have religious tests (or even care for that matter) for the politicians who run for office?

If I remember correctly in the Constitution it said that there can be no religious tests of ANY KIND for someone to run for office...yet, people are still harping about whether Obama's a Muslim, and I remember hearing that a majority of people still want someone as President with deep religious beliefs...what gives? I thought that there wasn't supposed to be any religious tests or anything!