Students bringing babies to class
A blanket ban on bringing babies to class is probably not allowed at many institutions. However, I agree that if the baby is acting up, then the supervising parent should take the baby out of the classroom so as to minimize disruptions to the overall lecture. 

This should be reached as an agreement outside of class time so that the lecturer is not placed in the position of having to stop lecture to ask the parent to remove his or her child from the room.