State laws requiring segregation of blacks from whites are another matter and are unconstitutional (14th Amendment). The feds have a Constitutional right to interfere with state laws that require segregation of blacks form whites.
However, the feds have no other Constitutional authority to interfere with any other form of discrimination on the state level and the feds have no Constitutional authority to interfere with the God given right of individuals and businesses to exercise their freedom of discrimination (freedom to choose) as they see fit.
“No shoes. No shirts. No service. Unless you’re gay or muslim.”