I deadlift and squat with just socks on. I keep my shoes off to the side and slip them on when I am changing weights so that I have some sort of protection if I drop a weight.
I'm not sure I fully understand the concern about hygiene. We use dumbbells, barbells, plates, machines that are rarely if ever washed which comes into contact with our shirts, shorts, legs, arms, etc. I don't know about you, but socks are the first thing that come off and go into the hamper when I get home from the gym...