One party is entering another party's home. If you're not comfortable with rules inside that home, then don't enter that home.
100% agree that whether your own home is shoeless or not is a personal and cultural preference and decision. More power to you. But if I am entering your home, then your rules prevail.
Since it is their house, they, and only they, get to decide the rules about shoes allowed inside or not.
Why is that guest assuming that their opinions are more important than the overwhelmingly accepted idea that people get to set their own home's rules?
> Maybe slippers are the answer?
The author explains in no ambiguous terms that they won't settle for slippers.
Are my guests regularly cleaning the bottoms of their shoe the way I regularly clean my floors? (Almost certainly not, because why would you?)
Why are you assuming that your guests’ shoes are dirtier than your floors?
They believe a floor mat would suffice and it's rude to expect people to get their socks or bare feet dirty from the floor.
Maybe slippers are the answer?