We're living in the age of paranoia. Not since the McCarthy era have we been so suspicious of our fellow man. We're convinced that every stranger's sneeze is a receptacle for H1N1, that the guy in line in front of you with the uncovered cough deserves corporal punishment. We've practically replaced our vanilla citrus shower gel with Costco-sized bottles of Purell. All for the fear of catching a little cold or flu that might ground us in bed eating soup and watching daytime TV while we moan to our significant others for a few days.
But this, this is f*@&ing ridiculous! How dare you assume that I am not clean enough to handle your child? That sign is so condescending and offensive that it actually makes me want to grab your baby, open its mouth, and sneeze into it. That's not right, I know. The baby is an innocent victim. I should really be sneezing into your mouth. Have we really reached the point where, because you have a child, you get to treat the rest of your peers like children? This sign says to me that you think I don't have enough common sense to realize that babies and children have weaker immune systems and are more prone to illness than we adults are. Basically, the sign says that you think I'm a dirty idiot.
What if I posted a sign on myself when I came into contact with your babies? "If your baby drools, poos itself, or is incapable of keeping its snot in its nose -- kindly back the hell up." After all, your baby is much more likely to be crawling with microscopic domestic terrorists than me.
I think it's pretty safe to say that unless you saw someone crawl out of a Jersey Shore hot tub, you can assume they're not going to spread disease onto your kid. And if you still think they (perhaps another child) are, then a simple verbal reminder -- "Hey, would you mind washing your hands, Carson's been sick lately?" -- is more than okay.