I have a pet peeve. It's actually a rather large peeve. I believe that people who ask me to take off my shoes before entering their house are rude. Not everyone is prepared to remove their shoes (holes in socks, complicated fastenings, foot odor, ugly shoes, ugly feet, orthotics).
Hosting is about making your guests feel comfortable. Comfort does not include asking guests to partially disrobe. Maybe you don't think shoes count, but you put them on in the morning not expecting to have to take them off later. If your house is so precious that you're afraid of dirt or your cultural heritage differs then don't invite people over or at least warn them that you expect them to remove their shoes when they are invited.
I also think that people who refuse to shake hands because they're worried about germs are being ridiculous as well. If you're that concerned, don't touch your face until you wash your hands. Though I will state I believe that what doesn't kill you makes you stronger when it comes to viruses. If you are really, really likely to become violently ill from a normal virus that would just give someone else the sniffles, then perhaps you ought to gear up like Michael Jackson in the surgical gloves and face mask.