I would never ask people to remove shoes, and have very rarely been asked to do so. Many of my children's friends used to take their shoes off (unasked) when they visited, but these days nobody does. I have a wooden floor in the hall, a stout doormat and a vacuum cleaner for the sitting room carpet. Very few people come to the back door, but we come in that way if we've been out in the car. The back door opens to a room at the back of the kitchen, where wellies and similar are kept, but now that we have neither dogs nor resident children they are rarely used. If I came in in muddy wellies, I might take them off, and of course I wouldn't dream of going to someone else's house wearing them, but it just doesn't happen nowadays.
I would be very averse to wearing someone else's slippers if offered, and whilst I might take my own if I were staying at a friend's house overnight, it wouldn't occur to me to take them if I went for coffee.
I tend to leave my shoes off when I'm indoors and walk about in stockinged (or bare) feet, but I don't take them off at the door - I come in, take my coat off, pick up the mail or whatever, go to the loo, get a cup of coffee, do whatever else is necessary before settling down, and then take them off in the sitting room to put my feet up. I wear slippers if it's cold, but am barefoot otherwise, unless I pop into the garden to hang our washing or put something in the bin, in which case I slip them on.