I think many see them as part of the fabric of the UK. Most are aware of their privileged status, but see it as mostly benign because they don’t hold power over laws, don’t think a republic would be any better for classism and like having a head of state who isn’t political. They can represent the country as politically neutral figureheads, which we likely wouldn’t have with an elected presidency.
This is not to say I like the royalty or am a royalist; I am not. However, there are many reasons people do support them which has nothing to do with being gullible, thick and seeing them as superior beings.