It’s not a belief, it’s a fact. And it’s part and parcel to the basic system of checks and balances underlying the US Federal and State Governments outlined in the Constitution. I had assumed it was common knowledge but I’m happy to walk you through it:
The United States Constitution guarantees a certain minimum level of civil rights. Each state’s Constitution may set forth a higher, but not lower, bar for civil rights. (California, for example, cannot amend the state Constitution to allow slavery or to prevent people with orange hair from voting. Well they could but the Federal Government would step in to stop the amendment from being enforced...)
Who is responsible for enforcing the Constitution? The Federal and State governments. So when a State government is the entity violating the Constitution the Federal government is responsible. It happens all the time and in myriad ways.
The executive branch (President, DOJ, various Federal agencies like the EEOC, etc.) can intervene if enforcement is at issue - usually with a lawsuit (for example, when a state violates voting rights) and rarely with force (like when states refused to carry out school desegregation following Brown v. Board of Education and Brown II). Likewise when the Federal government is infringing civil rights States Attorneys General will bring suit against the Federal Government just the same.
Congress, as the legislative branch, can also pass laws under the authority of the Commerce Clause to articulate a minimum national standard for specific civil rights like housing, employment, and education. I can’t post an advertisement for a job opening with the qualification “WHITE WOMEN ONLY” and the State of New York can’t either. States must abide the same way you or I are bound to follow federal law and the consequence of non-compliance is the same: the Department of Justice will come knocking to enforce the Civil Rights Act.
Finally, the Judicial Branch has oversight of state judiciary enforcement of civil rights. If Massachusetts arrests me without cause and a Massachusetts judge sentences me to prison without a trial I can appeal to a federal court that would then order Massachusetts to charge me or release me as the Constitution requires.
Our entire system is intended to allow the Federal and State Governments and the people to seek assistance and oversight to ensure the rights we are guaranteed are not infringed.