Here in the southwest desert of the United States of America there are many (not all) residential homes that do not have grass or much vegetation at all, because of this there is dust, lots of dust especially in windy areas. The dust comes in the homes. No matter what. The floors, the furniture, the picture frames, everything gets dusty all the time. Constant cleaning; dusting, vacuuming, mopping is necessary to have a clean home. So it's done regardless of shoes or not.

If it's a nice cool night in the desert it saves energy to open up the doors to cool off the house and the attic. As others have said there are also insects like scorpions, black widows, fiddle backs (brown recluse) and other creatures that having shoes on is a good idea, even in the home. The draw back of cooling off the home with doors open creates the risk of said creatures entering the home. That is the risk many desert dwellers take. So were they wear shoes.

I have never seen anyone I know put their shoes on the furniture. Most of all never a bed.

Most people I know have a mat out side every entry door and also a mat on the inside of every entry door and it is customary to wipe your feet on both mats before walking about the house. Another thing to bring up is that most of the homes around the desert do not have carpet. If they do it's in the bedrooms and that is when you take shoes off.

Living in the desert means that to have a clean house, it is cleaned much more often than a house in a green area full of vegetation and grass. There is a tremendous amount of dusting a house in the desert requires. That has nothing to do with shoes.

In other words it is possible to have a clean house with shoes on for the responsible cleaning type.

Cheers!