Sick people around your baby?

You're not in the wrong, you are just being protective. Depending on the sickness it could get your baby sick. If it's airborne then I wouldn't have them over but if it's not all they'd have to do is wash their hands and try not to cough or sneeze on the baby and it should be fine. Of course most people don't know if what they have is airborne or not so there isn't much you can do.