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.