I don’t know much about who all had access to the Pythia (the Oracle at Delphi) but certainly, the majority of her patrons were wealthy and even royal. I would not say everyone had access to her in practice. Many political attempts were made to control the Pythia’s sway, as she was so sought after. Much of her time was monopolized by those wealthy royals. She was in such high demand that at times they had to “hire” more than one Delphic Oracle. I think even Nero went to visit her once.

I’m so uncertain on the political independence and statehood of Delphi such that I will not address it. Sorry I can’t be more help on that matter.