Same here. I don’t wear outdoor shoes inside my house, but I don’t ask or expect others to remove their shoes. Maybe in Britain it is some kind of class marker, but elsewhere I think it is just personal preference. Some people don’t want to track in dirt and whatever else they have walked on during the day into the house.
In these parts some of the really old houses have “mud rooms”.
They are just small rooms by the entry way. They might have coat-hangers for winter coats as well.
You would take off your muddy or wet shoes and boots and leave them in the mud room to dry.
Then you kept another pair of clean shoes in the mud room to put on before going in the rest of the house.