Freedom Frog, here in MI we have had a number of people badly injured and killed because they were blowing off fireworks.
JD is right in that they are not hard to control, unfortunately, too many people are just plain dumbasses and have no freaking clue how NOT to get their head blown off (as in the case of a woman last year who stuck her head OVER the thing when it didn't go off. When it did.....well she's dead now and her son watched the entire thing).
Point being: Yes there are non professionals who know what they're doing. But too often, they don't.
We had neighbors next door blow off some real pretty, real illegal stuff their first 4th of July. They blew them off feet away from our bedroom windows, scared my dog, scared my daughter and they honestly didn't care. The following year, the people behind us blew them off and there was really little room between our homes. When they were asked to stop doing it, they copped an attitude. Too often, people who want to blow them off have really given little to no thought to the area in which they are playing around and honestly only care about their own fun.
In this day and age, neighborhoods are not very close knit and people really have no idea who lives next door to them or behind them. They know little about the neighbors with the autistic son or the person struggling with an illness. They are quite often consumed with their own needs and desires and do not take into consideration their surroundings before making the decision to have the fireworks show.
This is NOT always the case. There are times still where neighbors have a close knit relationship to where it's become a neighborhood tradition. However, as you said, you don't know these people that well and without having answers to the above questions it's perfectly okay to be the bad guy and say no.