The school's basic function is to be a place where children learn and grow - and play is an important part of learning and growth. Anyone who buys a home near a school does so with knowledge of the school's presence, it's function, and it's "customers." If you buy a home near a school, you should expect the presence of many, many children and their parents - and all that entails. You should not expect the pre existing school to change it's basic purpose when it was there first and you bought an adjacent home willingly.
Some restaurants are built specifically with children as patrons in mind - fast food restaurants with playgrounds, Chucky Cheese and other restaurants like that. If you go to such a place, you should expect lots of kids and lots of noise - those are the patrons that the restaurant is catering to.
Other restaurants are geared toward other patrons. But even "family friendly" restaurants are built with the goal of providing a pleasant dining experience for ALL patrons. A screaming, disruptive, crying child is not happy - and neither is anyone in the immediate vicinity. Parents have the responsibility of being good, thoughtful citizens and sometimes this means that they should remove noisy, disruptive children from the presence of others, so that others can enjoy an environment they're paying for, without someone else's screams intruding on them.
Simply put - it's the right thing to do. And when people are so rude or obtuse about what is RIGHT to do, sometimes others must step in to correct the situation, unfortunately.