One unavoidable fact is that certain parents are overly invested in their children, believing that their child somehow "winning" whatever it is they're supposed to be doing at the moment means they're better people. When you tell these parents where your child is attending school, they'll be mad. That's their problem, not yours.
The nice thing is, things like this help you identify the members of the crowd who are deeply awful people, because until triggered, some are pretty good at hiding it.
But yeah, definitely do NOT go on and on about it, or volunteer the information unasked, unless you're interested in revealing that the awful person in the room is you.