This is a mindset thing, a cultural thing.
I don't know the ins and outs of the northern European/Japanese attitude to shoes indoors, but I suspect here in the UK it's not actually about cleanliness, it's about social class. (Objectively, people who leave their shoes on indoors aren't stricken with disease from all the nasty "outside" that they "bring indoors". People have doormats and hoovers to deal with dust and dirt.)
In my mind, this is an aspirational working class/lower-middle class suburban mindset: bungalows, 70s estates with wall-to-wall carpets and cans of air freshener in the toilet. If you cycle back from your job lecturing at the university and wheel you bike through your 2-up, 2-down terrace to hang it on a rack in the kitchen, you're not worrying about shoes-in-house.
I imagine it in from people who are more likely to eat their lunch in a garden centre than that super-nice new Korean small plate place that the Observer was raving about.
I think it's indicative of people who think that "outside" is generally dangerous, alien and scary.
I bet it's a near-perfect parallel with voting for Brexit, where we know that income or geography weren't the most consistent drivers, but:
What united Leave voters in focus groups in the run-up to the referendum, he says, was support for a whole set of "traditional" values.
"They tended to value things like order, stability and safety against things like openness, modernity and other social-liberal values that were more popular among Remain voters. Often it's about harking back to the past - sometimes a feeling that they don't belong to the present."
I certainly think it's rude to keep your shoes on in a house where they don't want you to, and it's up to guests to spot these class- and mindset-markers that will tell you that this is that kind of place.
But it's perfectly reasonable to not offer to take your shoes off when you arrive at someone's house where that rule is clearly not in place. In the complex social dance of the English class system, you could be accusing your host of being petty/suburban/Hyacinth Bouquet.