Intel Management Engine is abbreviated as IME, and AMD Platform Security Processor is abbreviated as PSP. Those are each same abbreviation as Input Method Editor, a mandatory keyboard input layer for East Asian languages, and PlayStation Portable, Sony’s game console which cryptographic security is famously hacked, by the way.
That can’t be coincidence. Those are names intentionally chosen to make technical information hard to search for.
So a “clean” CPU can only be built outside of sphere of influence of whichever agency managing IME/PSP, and of course has to be free from its Red counterparts as well. I don’t think that will happen naturally.