What was the constitutional background of the Civil Rights Act of 1964?

The ideas expressed in the Thirteenth and Fourteenth Amendments, as well as the principles embodied in the Supreme Court’s landmark decision in Brown v. Board of Education of Topeka (1954), are certainly relevant in the decision-making process that led to the Civil Rights Act of 1964 ultimately being passed by Congress. However, the ensuing legal battle concerning the constitutionality of this Act revolved around the interpretation of the Constitution’s Commerce Clause.
With the Lochner Era coming to an end during the New Deal, the Supreme Court began to expand its interpretation of Congressional power under the Commerce Clause. In decisions such as Nebbia v. New York (1934), West Coast Hotel Co. v. Parrish (1937), and Williamson v. Lee Optical of Oklahoma (1955), the Court ended the policy of economic due process that had curtailed the ability of Congress to legislate in the realm of economic activities. The Supreme Court addressed the extent of Congressional Power under the Commerce Clause in Wickard v. Filburn (1942), holding that Congress could impose national quotas on wheat growers no matter the size of the farming operation under the theory that in the aggregate all the small operations might affect the overall national market.
These decisions provide the constitutional backdrop to the Supreme Court’s ultimate decision in Heart of Atlanta Motel, Inc. v. United States (1964). The owner of the Heart of Atlanta filed suit arguing that Congress exceeded its authority under the Commerce Clause in enacting the Civil Rights Act of 1964, that the Act violated the Fifth Amendment’s bar on deprivation of property or liberty without due process of law, and that the Act violated, in a twist of irony, the Thirteenth Amendment’s ban on involuntary servitude. The decision of the Court was unanimous in upholding the Civil Rights Act of 1964, although some of the Justices had differing rationales as expressed in three concurring opinions.
The decision in Heart of Atlanta held that the passing of this aspect of the Civil Rights Act of 1964 was a valid exercise of Congressional power under the Commerce Clause as applied to a place of public accommodation. For further information regarding the passing of the Civil Rights Act of 1964 and the related constitutional backdrop, the Heart of Atlanta majority opinion written by Justice Tom C. Clark contains a well-written synopsis of the history of the Act.

The passage of the Civil Rights Act of 1964 was climax of a century-long conflict between those who supported the concept of citizenship and Constitutional protection for every American, regardless of race, and those opposed to that concept.
Slavery was abolished with the passage of the 13th Amendment, which was ratified in December of 1865. The 14th Amendment, which was adopted three years, decreed that all citizens, regardless of race, were entitled to equal protection under the law.
But state and local governments, particularly, but not exclusively in the South, adopted laws, often called Jim Crow legislation, which in effect made their black populations second-class citizens.
Public facilities, such as restaurants, movie theaters and stores, were legally segregated in many Southern states and the concept of "Separate but equal" public facilities was upheld by the Supreme Court in 1896.
The High Court reversed itself on that issue in 1954 in Brown v. Board of Education when it declared that separate educational facilities for blacks and white students were inherently unequal.
But the decision did little to impact other forms of discrimination.
President Kennedy proposed a major civil rights bill in 1963. Following his assassination, President Johnson took up the issue and pushed what became the Civil Rights Act through Congress despite vigorous opposition from Southern lawmakers including many of his fellow Democrats.
The Civil Rights Act was signed into law by President Johnson in July of 1964. It outlawed discrimination on the basis of race, religion, national origin, or sex.
It is considered one of the most significant pieces of legislation ever passed by Congress.

At the heart of the Civil Rights Act of 1964 was the constitutional interpretation of the Thirteenth and Fourteenth Amendments. The primary focus was on the role of states to create discriminatory Jim Crow laws that reinforced white supremacy through their "separate but equal" policies.
The Plessy v. Ferguson (1896) ruling dictated that states had the right to create and implement such policies. This created a social strata that was akin to the white dominance under slavery, which could be argued as a violation of the Thirteenth Amendment. The states were creating laws that relegated African Americans to the status of second-class citizens, a clear violation of the Fourteenth Amendment and its equal protection clause.
Ten years prior to the passage of the Civil Rights Act of 1964, the Supreme Court had ruled that “in the field of public education, the doctrine of 'separate but equal' has no place. Separate educational facilities are inherently unequal.” The court's ruling in Brown v. Board of Education of Topeka (1954) set a precedent of the federal government ruling against discriminatory practices in all circumstances, which paved the way for the passage of the Civil Rights Act of 1964.
https://www.nps.gov/articles/civil-rights-act.htm