The Constitution also states that Congress shall make no law regarding an establishment of religion (or something along those lines). Doesn't stop politicians from trying to introduce "Christian" legislature or claiming that America is a Christian country.
Keyword is "trying". That's what the Supreme Court is for. They're the ones who are intended to dismiss legislation that contradicts the Constitution, and so far they've done a decent job separating church and state. Not as well as they could have (One Nation, Indivisible...), but certainly better than how things would be without them. As for claiming that America is a Christian nation, that's just free speech. It's stupid and inaccurate, but doesn't have any legal authority either.
I mean, if I wanted to, I could claim that America is a communist dictatorship, but that doesn't do anything to make it true.
It may be the majority religion here, but that still doesn't make doing the above things legal.
I'm questioning just how much of a majority Christianity even is anymore. There are a lot of Americans who call themselves Christians but do basically nothing to back that title up. The actual participation in religion is lower than the polls would have you believe, especially in cities.
Still, those laws are unconstitutional, even if they hold no power. The First Amendment, combined with the Privileges or Immunities and Due Process clauses of the Fourteenth Amendment, means that those laws need to be removed.
They aren't laws. They're constitutional articles, and that's different. A constitutional article can only be changed by an amendment, not a legal challenge. Neither Congress nor the Supreme Court may overturn part of either the state or national Constitutions, although the former vote upon amendments.