This is pretty much what I grew up with - some of the things in this thread are completely alien to me especially in terms of it being manners
I only started encountering it after decades of life and then only when someone had a swanky new carpet. Once it had been down for a bit, it was shoes as usual.
Firstly, your feet must hate you

Mine can't wait to be out of their shoes. Esp horrid formal work shoes, which are just sweaty and awful.
Ahhhh.... so it's just that people cannot afford decent shoes, then?
Issue combat boots. Best things ever.
I have studied bacteria/infection and it is very important not to wear outside shoes around your home - don't let anyone else do it either. Bringing in dirt into your home from pavements/garden is dreadful and it will cause infection.
Are you one of those sickly people at the office who always gets the colds and coughs?
We played barefoot in the dirt and mud and filth as kids. Long as we didn't traipse huge quantities of mud through the house and into the carpets, we were good. Last time I had a day off work was from a road crash. Can't remember the last time I was ill or infected with anything. I don't even have any allergies.
Some people don't like taking their shoes off but tough, they tend to be the blighters that don't respect the fabric of your home and they are not civilised.
I'm not Japanese, I don't jump in puddles of animal poo and I am capable of using a vacuum cleaner. Why would I take off my shoes?
If you have some swanky fancy new rugs, then say so, but otherwise it's just weird...
I was once at a B&B in the Isle of Skye and they had us take our shoes off at the door, that was weird.
So people want shoes off when entering *their* house, yet claim other people wanting the same is "weird"...??!!
If it really was as rude and uncivilised and disgusting and horrid as everyone is claiming - Why don't hotels, restaurants and shops have the same policy?
Why would you give me the strangest look if I wanted your shoes off before you got into my nice clean car?
Why should I assume that your home is clean enough to walk around in without shoes on in the first place... when I know from experience that many people's homes ain't as clean as they think?