For one thing, the Queen was rich for a list of complex reasons that largely have to do with hereditary properties and assets stretching back centuries. It's not as cut and dried as "taxpayer expense". Yes, the monarchy as an institution benefits from certain public resources, just as do all institutions in all major countries, but it doesn't do so to any obscene degree compared to a vast range of other public projects and organizations that waste enormously while being much better funded. Any major head of state also benefits enormously from taxpayer money in all sorts of ways and lives daily in the lap of luxury with enormous resources spent on his or her security, personal living "needs" and any trips they make. Despite this, I see little complaint about that much larger source of taxpayer money being spent.
There seems to be a reflexive, emotional and partly irrational hatred of the UK monarchy spending heavily and having assets and money, along with certain public benefits (which by the way are carefully circumscribed) by people who barely bat an eye at the fact that the absolute largest sources of resource and tax spending on a vast range of immensely expensive but often wasteful and even pointless things are perfectly modern government institutions that have nothing to do with monarchs. It's an absurd sort of blindness.
What the UK government spent on the idiocy of the Iraq War alone far exceeds all public funds given to the Monarchy in decades, but hey, let's complain about Elizabeth and the castles that have been in her family for centuries.