If you can bear it and have the patience, I'd go with the flow on this one. With a bit of luck you'll find that you can impose rules at your house (in a fun way) that are completely different from the way the boy would behave elsewhere ...... probably by use of bribery of the food variety that they both will receive if there is for example, no bouncing on the sofa, no swearing etc etc. Maybe you can make it sound as though the rules are not specially for the benefit of the other child but general houserules that apply to all occupants and visitors.
I have experienced this from the opposite end from you ( and my child is not misbehaved, an incident was completely misinterpreted by another parent I think). And in a small school, low number of children, small number of parents it's painful in lots of different ways for both the child and the parent. And over time the children get the friendships they want anyway. It's prob best to take the approach that you like whoever your son likes as there must be something good about the person for your son to like them, and then just see what happens. If really they don't get on, the friendship will fade over time, but if you try to manipulate the situation it could blossom much like a forbidden romance.
Sorry if I'm sounding preachy, or like the wise old woman of the hills.
You may have clearcut reasons to be unhappy with this particular friend, but there will be greyer cases of what is desirable / undesirable, and once you start doing this kind of freezing out of some children and others it becomes a difficult path for you too as you will be forever analysing what is OK and what is not (unless of course we are talking about law breaking above the age of legal responsbility).
You could have a massive positive influence on the other child and family (and a new sofa into the bargain).