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?