To answer this question as well as your other question, here are three points to consider:
Most Americans drive just about everywhere. So their shoes just don't get very dirty. You don't pick up much dirt driving to the store, walking around in the parking lot and in the store, and then driving back home. So American floors don't get very dirty compared to places where people might walk everywhere.
If you're living in an urban or suburban environment, most surfaces, whether streets or sidewalks or parking lots, will be paved. So you won't pick up dirt on your shoes from walking there the way you would if these were dirt surfaces.
Most American buildings, whether homes or offices, are air-conditioned. In addition to cooling the air, an air conditioner usually filters the air as well. This removes the kinds of particulate matter that might otherwise accumulate.
So with all of these considerations, wearing one's outside shoes inside is really not a big deal. There will still be some families who take their shoes off, but you're extremely unlikely to catch horrible diseases, or even to get your feet dirty, if you walk barefoot on a floor where others have been walking with their shoes on.
If anything, the problem in America may be the reverse: Things aren't dirty enough! There are theories that allergies are such a problem in America because our immune systems don't learn to distinguish between genuinely harmful matter and everyday things like dirt or smoke or pet hair, and so the immune system ends up overreacting to everything.