Background: Washington, D.C. is not a state and in theory the US Congress performs state legislative practices for it. In practice, Congress has devolved civil policy to a mayor and devolved state court functions to a superior court.
Purple door disputes wouldn’t be a Federal issue, but one of the D.C. superior court. The Feds have only intervened four times, and it was over much bigger features than HOAs. And the Supreme Court has actively closed loopholes where local issues relevant to any other state could become Federally interesting.
The Federal government could not pass a law prohibiting me from painting my front door purple (that would be an infringement on my 1A rights).
As I understand it, an HOA can enforce such a prohibition as a private entity (and use the courts to back them, ultimately).