I think anyone who doesn't grasp the intrinsic difference between kids playing sport in public, and a demo that is deliberately designed to garner media attention, probably needs their heads examined.
Personally I'm uncomfortable with people taking pictures of my children, if we go to a public event and we see someone taking general pictures of the event, rather than just someone taking pictures of their own kids with ours just randomly in the background, we'll give them a swerve. Our kids don't have their pictures on the school website, their pictures don't go on Facebook or Instagram.
There is a nuance here - for me, a picture of a scene (say a street festival) which contains children, or adults who haven't consented to having their picture taken is different to picture of a specific child within that scene. So, in the OP case, taking a picture of a football match with shows 50yards of pitch and dozen kids is different to singling out a specific child and taking a picture of that one child - the first is a picture of a football game which happens to involve children, the second is a picture of a child.
Despite that nuance, I absolutely take the view that my image (or my children's, or anyone else's) is not available for others to use as they wish - I find the assumption/assertion that it is extremely bad manners, and that to continue to photograph it despite being asked not to is incredibly offensive.