The Constitution determines eligibility, not the States crybabies.
Actually , Congress is instructed by the Twentieth Amendment, Section Three to determine whether or not the President Elect shall have qualified to be legally President or they, Congress, must name someone who is qualified. By the term shall have qualified, they can only be referring to the eligibility requirements in Article Two. This means it is the job of Congress to enforce those requirements or we end up with a usurper to the office of President. A usurper is not a President nor can ever hold the office of President. We are told this in plain language right there in the eligibility requirements themselves as they start out with the two words, NO Person.
If you are not eligible and Congress does not enforce the Twentieth Amendment, Section Three, those two words all by themselves keep you from being a legal President. Congress did not enforce the requirements and thus broke their oaths to support the Constitution.