You have the cases wrong and mixed up. Morrison case you cite is a Commerce Clause case which limited the reach of Congress' power, because the law in question - Violence against Women Act - had nothing to do with interstate commerce.
The court upheld the Civil Rights Act of 1964 under the Commerce Clause because the Commerce Clause was what the Congress relied on to enact the law. (Heart of Atlanta motel v. U.S.) In other words, the court had no occasion to render judgment on federal power to prohibit discrimination on any other ground (Edit: There is another area - voting rights, which are explicitly provided by the Constitution).
On State level, the SCOTUS generally does not get involved in anti-discrimination laws because all the states have boiler-plate anti-discrimination laws that are enforced by State governments. But when State laws discriminate against individuals/groups on prohibited grounds (race, sex, national origin, etc.) the SCOTUS itself gets involved, quite actively. What do you think Brown v. Board of Education was about?
I don't have the cases wrong or mixed up. In case my point was unclear, I'll restate it: The Supreme Court has explicitly ruled that businesses are not bound by the Fourteenth Amendment. Discrimination by businesses is only illegal today because of laws passed by Congress; if those laws were repealed, victims of discrimination would have no recourse in the courts. There is no Constitutional protection against discrimination by a business.
In 1875, Congress passed a Civil Rights Act that was very similar to the Civil Rights Act of 1964. The key difference is that Congress defended the 1875 law with the Fourteenth Amendment's Equal Protection Clause rather than the Commerce Clause. In the
Civil Rights Cases, the Supreme Court ruled that the Fourteenth Amendment only applies to state actors and cannot be enforced against businesses, and declared the Civil Rights Act of 1875 Unconstitutional. This allowed businesses to openly discriminate against blacks for the next 80 years.
US v. Morrison is directly related to that decision, as Congress defended the Violence Against Women Act with both Commerce Clause and Equal Protection Clause arguments. In section 3 of
the opinion, the Court explicitly reaffirms the
Civil Rights Cases and again concludes that "Congress' power under §5 [of the Fourteenth Amendment] does not extend to the enactment of §13981 [VAWA]."
Brown v. Board of Education further reinforces the point; it only integrated government-run schools, and private "segregation academies" became popular in areas opposed to desegregation.