... any given state constitution must also conform to the US Constitution.
^That is a correct statement:
THE UNITED STATES CONSTITUTION
Article. VI.
Clause 2: This Constitution, and the Laws of the United States which shall be made in Pursuance thereof; and all Treaties made, or which shall be made, under the Authority of the United States, shall be the supreme Law of the Land; and the Judges in every State shall be bound thereby, any Thing in the Constitution or Laws of any State to the Contrary notwithstanding. [Link]

