"Separation of church and state", as a specific quote or concept, is nowhere in the founding legal documents of the United States.
It was no less than Thomas Jefferson who said:
Believing with you that religion is a matter which lies solely between Man & his God, that he owes account to none other for his faith or his worship, that the legitimate powers of government reach actions only, & not opinions, I contemplate with sovereign reverence that act of the whole American people which declared that their legislature should 'make no law respecting an establishment of religion, or prohibiting the free exercise thereof,' thus building a wall of separation between Church and State.
Next, your strawman:
It's use did not create prohibition against religious expression.
Correct. Still doesn't. You're legally entitled to say "blacks are of the devil" (or whites for that matter). Go ahead! No government agency will stop you. However, you're not allowed to discriminate based on race, color, religion or national origin in hotels, motels, restaurants, theaters, and all other public accommodations engaged in interstate commerce (court-upheld interpretation: pretty much anywhere).
No one believes that any of our rights are unlimited. You can speak your opinion, but you can't yell fire in a theater. You can bear arms, but don't expect to own a nuclear bomb. You can sincerely believe that whites are a superior species to blacks, but you don't get to own, kill, intimidate, lynch, or otherwise harm a black guy, regardless of your vile beliefs. This isn't something I'm making up out of whole cloth, but well-established and widely accepted interpretation of Federal law.
Documents which govern the FEDERAL government do not necessarily apply to State or Local governments.
Read your Constitution, son. The 14th amendment says:
Section 1. All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside. No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.
This codified previous Constitutional supremacy thoughts by explicitly stating that States don't get to write laws violating the Constitution or selectively affording privileges to one group and not another.