AFAIK wearing outdoor shoes indoors is mostly an American thing, especially within big cities/on the coasts. As a midwesterner, shoes always come off at the door, who knows what you stepped in.
It's ultra common in many european countries. I've got one friend where the rule at his house his "shoes off" but most others keep their shoes inside.
It's also highly common for people living in houses to have a "shoes on inside, but only on the ground floor" and shoes off upstairs.
So I guess YMMV.
I (n=1) don’t wear outdoor shoes at home but I’ll allow my guests to keep them. I’ll clean when they’ll leave.
When I’m at home I can wear slippers but my guests can’t so I allow them to keep their shoes.
Scandinavia, Germany and down to the metiterranean and everything east of incl. Croatia I think it's all shoes off?
IME it's not common in european countries but guests tend to not be required (though it's usually appreciated), hosts usually won't provide slippers, it's not standard to bring your own (though it's often appreciated), and you won't be required to walk in socks.
Here in the south, the majority of people wont ask visitors to do so.
I assume (as always...) that by "European" you mean "western European", because in Romania you wouldn't be caught dead wearing shoes inside.
(FWIW: midwestern American, I take my shoes off at the door usually but have no problem walking through the house with them if I’m e.g. grabbing something I need or going from the back yard to the basement. We have three dogs who are much dirtier than my shoes are going to be.)