Goldwater and SJoyce: the Civil Rights Act of 1964 was perfectly legal under the Constitution. The Equal Protection Clause of the Fourteenth Amendment states that Congress may pass any law to ensure equal protection under the law. That predated the '64 CRA by nearly 100 years.
Relevant portion emphasized. It's not creating equality under the law, it's regulating private conduct.
In some cases, that's necessary. If it was unconstitutional, then why have I never heard of any legal challenges to it? And even if it regulated private conduct, then how did it not establish equal protection under the law? The Fourteenth Amendment says that Congress can make
any law necessary to ensure equal protection. No ifs, ands, or buts. No exceptions.