Federal law supersedes state law based on Article VI to the U.S. Constitution, which declares the Constitution and the Laws of the United States as the Supreme Law of the land. Except for issues that Federal banking regulations cede to the states, e.g., usury laws or foreclosure proceedings. the states have no ability to regulate the actions of a national bank, a Federally chartered savings association or a Federal credit union. For example, the state of Texas forbade chartering of state banks from admission into the Union until 1903. During that period, national banks operated in Texas unrestricted by state laws.
You know what I do for a living? I work in risk management with major banks. Believe me when I tell you banks are very much subject to all kinds of state laws. They can be inspected by state auditors. Cuomo when he was governor of NY threatened the banks with exactly that in order to get them to support gun grabbing. If NY can do it, other states can lean on them in the opposite direction using the exact same means.