You are totally misinterpreting Article 6, and attempting to apply it in an irrational and illogical way, to presidential appointments to the cabinet. It just does not apply in that case, because the appointment (pursuant to the Constitution) is made BY THE PREZ! Nowhere does the Constitution say, the president has to consider ANY factor, it is UP TO THE PRESIDENT! When he does pick someone, he isn't going to tell you all the reasons he picked them or all the reasons he didn't pick someone else, he will simply say, as most do... that he picked "the best man for the job" and hopes Congress will approve his pick. You keep trying to manipulate Article 6 and have it apply here, when it can't apply here, it's impossible to enforce it. If the president picks a Baptist, has he discriminated against a Muslim who was equally qualified? Did the president consider all 350 million Americans to determine he had picked "the best man" for the job? How do we know he hasn't discriminated on the basis of religion in his pick? We just take his word for it that he didn't, or what?
Article 6 is specifically to prohibit the government from establishing religious tests for people seeking office. In other words, Congress can't pass a law that Muslims can't run for office or be appointed to public office. The president reserves the right to use whatever judgement he wishes in his appointments, and as I said, it most certainly CAN include his religion, religious beliefs, race, gender, or anything else.. the choice is the president's choice to make, according to the Constitution.