This is true that they’re not being supported by taxpayers, and arguably that’s the single biggest distinction. Technically, institutionally, nothing has changed or will change if Harry is splashed on the front page of the daily mail arriving at a Well Child event with police presence/security (if he gets what he wants), members of the public held back by metal barriers, striding to meet the CEO with outstretched hand and enormous grin - whereas at best you’d find a few shots of Beatrice or Eugenie gurning inside a gallery or at a photo call indoors somewhere, halfway down the sidebar of shame.
But in terms of what really matters, the public perception that had people queueing day and night to file past QE2’s casket, that saw football fields of flowers outside the gates of KO when Diana died, the thing that in the modern era allows the monarchy to continue, public perception counts for far more. The monarchy’s PR and media budget (time and money) is testament to that.
Harry considers himself Diana’s heir, she being the self-proclaimed Queen of Hearts. He will be viewed by the public, the people by whose grace the monarchy still exists, as Royal and carrying out (some) Royal functions. Meanwhile, there they will be back in California, trading off this very same royalty or trying to.
I don’t really know what can be done about it. They won’t be present at any banquets, diplomatic functions, state occasions, military events etc. Will that be enough to distance themselves enough from the RF so as not to be able to trade off/profit financially of their royalty? I’m not so sure.