Not one affected by the restriction on state action in the 14th Amendment.
> and cannot continue to give funding to these schools if they continue to use affirmative action.
Yes, it can (this is obvious, since the decision itself explicitly allows the federal government itself use race-based criteria in its own admissions at the schools it runs, notably, the military academies) and it can change the terms of the Civil Rights Act of 1964 so that the interpretation of the 14th Amendment limits on state action that the Supreme Court imported to it due to textual similarity are not imposed on recipients of federal funding.
Either way I'm happy with today's ruling and look forward to everyone getting a little more equal treatment under the admissions process.
No, accepting federal funds doesn’t make them government actors, nor does it subject them, particularly, to the Constitutional provision here (which binds neither private parties nor the federal government, but only the states.)
They are bound by Title VI of the Civil Rights Act of 1964, though, and the Court has a history of interpreting the language of that statute through the lens of its 14th Amendment jurisprudence regarding similar language, which it followed (while altering the guiding jurisprudence) in this case.