Are you in the UK? The monarchy and House of Lords are an obvious anachronism and they need abolishing [1], but I would say it's a very small minority who care who you parents are/were (mainly people who think their own parents are/were a big deal) — and a similar small minority who might also ask "which school did you go to?".
[1] e.g. https://www.sortitionfoundation.org/
Chances are, they're still running the country in some capacity. (The example I'm thinking of was a Duchess. Her descendant was a beak at Eton who taught Boris and the haunted pencil).
Also, Victoria is only about 100 years ago. I suspect power and wealth are pretty strongly hereditary over that time span in many other democracies.
People with Norman names wealthier than other Britons
People with "Norman" surnames like Darcy and Mandeville are still wealthier than the general population 1,000 years after their descendants conquered Britain, according to a study into social progress.
https://www.telegraph.co.uk/news/newstopics/howaboutthat/842...
(Obviously the discrepancy has to start with the Conquest, I'm just saying that strictly speaking you can't use that paper to support that conclusion).
(Alec d'Urberville in "Tess of the d'Urbervilles" is a nouveau riche person who adopted the name rather than a descendent of the original d'Urbervilles. Probably that happens in real life, too, though I expect the people who did the study have taken that into account and have done the best they can in the absence of reliable public ancestry data.)
My source was the Sutton Trust and Oxera.