What does "under the United States" mean? No test shall be required in any *federal* capacity, or in *any* capacity? I'm not so sure that all the first section of what you posted (which clearly refers to the State Legislatures etc.) carries over to the second.
I'm no Constitutional Scholar, but the reason I'm sticking on this point is that it's hard for me to see how the religious tests for office that clearly existed in the Federal period were not struck down immediately by Article 4. Also...how would article 4 have passed in the first place if there were states who had such tests for office?
Something's not jiving here.
I think it clearly does. It applies to any position of public trust in the U.S., be it at the federal, state, or local level. If you look at Article I, Section 6 it says that "No Senator or Representative shall, during the Time for which he was elected, be appointed to any civil Office under the Authority of the United States which shall have been created, or the Emoluments whereof shall have been increased during such time; and no Person holding any Office under the United States, shall be a Member of either House during his Continuance in Office." The second half of that clause has always been interpreted to mean that you cannot hold office in Congress if you are also holding office at any other level. Can't be a state senator and a U.S. senator, or a mayor and a congressman, or a state judge and a city councilman. "Under the United State" in Article VI undoubtedly means the same.
For it to be struck down someone would have to sue and the matter taken through the judiciary to the Supreme Court. For the first 150 or so years there was a bias towards Christianity and such laws didn't attract much opposition, if any. Things have changed.