No. It is.
Think of the U.S. Constitution as a contract or pact between the states and the newly formed federal government. The states are keeping certain powers and ceding others to the federal government. The Supremacy Clause you're referring to says that this contract (or pact) is supreme -- it overrides any other contract (eg., the prior Articles of Confederation).
Whatever is in this new contract (called the U.S. Constitution) is now the supreme law of the land. But the contract never stated that the BOR applied to the states. The first amendment, for example, specifically says "Congress". Now, how can the Supremacy Clause apply the first amendment to the states as "the supreme law of the land"? It can't.
Anything in the U.S. Constitution that only applied to the federal government (like printing money) only applies to the federal government -- do you think the Supremacy Clause means the states can print money?
The first eight amendments, when written, only applied to the federal government. The Supremacy Clause does not change that fact one iota.
*buzz* Wrong! "We the People" didn't like the way the Confederacy was going, so we got a bunch of our best and brightest together and had them revamp things. We gave certain powers to the FedGov, left the rest up to ourselves and our State governments, and added a BoR to let EVERYONE know what was hands off to anyone.
...
Accept for the parts where is says "laws of any State to the contrary notwithstanding" and "and the Judges in every State shall be bound thereby" and that the prohibitions in the 3rd, 4th, 5th, 9th, and 10th Amendments means only people who are living in Federal housing, own Federal property, or are being tried in Federal courts...
You can't win this one.