i love touching quilts - there is something about the texture of them, looking at the stitches, esp of hand quilted quilts that seeing them up close is cool! Granted, i make sure that my hands are clean, i haven't eaten a bag of chips while walking around or just finished a messy chocolate brownie.
If you don't want people to touch the quilts, place them far enough back w/ a rope in front of them that people can't get up close enough to touch them, but can only admire from a distance. Quilts have lasted for centuries being touched, loved on and admired by many.