Kind of. When Congress passed the Civil Rights act in the 1960s, the courts became much less aggressive in finding racial equity in the US Constitution, because it simply wasn’t necessary.

Private high schools that had segregation policies ran the risk of having their tax status revoked messed with by the IRS.

Colleges get tons of money from the federal government, which is conditional on not discriminating - and keeping federal government happy.

So private secondary schools still have a fair amount of leeway. Not infinite, but in reality they don’t have to worry about lawsuits like this.

Colleges do.