The shoes thing is very much regional. I'd wager houses in the areas of North America and Western Europe where it's not conventional to take of your shoes aren't any dirtier than houses in areas where you do. Then there's the sweaty stocking feet issue. We think it's perfectly normal, but in other parts of the world it's considered disgusting to let someone's stocking feet touch your floor. And of course, some people wear shoes and sandals without socks. You'd really prefer someone walking around your house in bare feet?
Here's an article in the UK expressing anxiety about the growing trend there for removing shoes, which many regard as a rude imposition on guests:
http://www.dailymail.co.uk/femail/ar...sary-naff.html
And another article for expats trying to understand the social norms around shoes and how they vary by country:
http://expatsincebirth.com/2013/11/2...-shoes-please/
And an article in the U.S. where removing shoes at the door is described as a practice started in Hawaii that is making its way into the mainland:
http://www.staradvertiser.com/news/2...ks_others.html