My understanding is that they are to some extent, at the beck and call of the Queen, though. For instance, that they couldn't marry without royal consent until Charlotte was born (pushing them down the line). It seems like they are all essentially kept waiting to be told what to do, what to turn up to. It would take a LOT of strength of character (and training from your parents) to say NO, ACTUALLY, I CANNOT BE AVAILABLE FOR X ROYAL EVENT ON THE 24th, I HAVE A JOB AND CAN'T GET THE TIME OFF.
Even Zara T is essentially self-employed, and can work around "royal hours".
We don't know what goes on behind closed doors, and we don't know what the consequences would be for Beatrice or Eugenie if one of them had a high-earning, mainstream, restrictive job at, say, BCG, and simply said no. We know already that the Queen even dictates the length of Kate's hemlines, so I think that when granny is the reigning monarch things are a bit different when it comes to sending out CV's.
Hauser & Wirth is a very cool place to get a job, and they don't need the cache of a royal employee to be one of England's more impressive galleries. I don't imagine she earns very much (she was only on 25k or something in her last job), but at least Eugenie is doing something, unlike Beatrice.