You might get harassed, but if you stand your ground, you cannot get convicted for taking pictures of children in a public park. State and local statutes must respect all of the legal rights that are owed to a person. The Due Process Clause of the Fourteenth amendment serves as the means whereby the Bill of Rights has become binding on state and local governments as well as on the federal government. Just because a town passes an ordinance, doesn't mean it will stand in court.
You may get the cr4p beat out of you by a father and the local authorities may look away, or they may trump up other charges like disorderly conduct, or make touble for you in any number of ways; but a court will not convict you for taking pictures in a park. If you start taking lascivious shots of children, that's another matter.
Again, though, I will say, just because you can does not mean you should; there are also no laws against passing gas in a crowded elevator -- but we all know you shouldn't do it anyway.
To continue on this subject. It's rare, but it happens, even if you are at a public event wearing a Domke vest, carrying two cameras, one with long lens and monopod. "Why are you here? Who do you work for? Why are you photographing these little girls? I don't want you taking pictures of my daughter!"
For that woman, my reply was simple. "They are my granddaughters."
But I also had been shooting record shots of the girl's dance presentation at a show that had many studios showing off their skills. Her daughter was actually in the same school, but different level than my grandgirls and I told her that all photos went to the teacher to do with as she wished, so she should ask her about what the photos were used for.
In the US, there are few restrictions on what you can shoot in a public place, unless you are a wierdo shooting up skirts, of course--a local guy is in jail for doing that twice, now, at Target where he was arrested, and a week later at Walmart after being released on bond. Little girl's dresses, too. So, hopefully, they won't bond him out this time.
In Europe they have new, stricter laws regarding one's right to their own image. And people are very aware of it. Children love to climb on the statue of Peter Pan in London's Kensington Park, for instance. When I was there I was very careful to ask permission of the parents before taking a photo of the scene.
Farther on I came across the Hyde Park memorial to Princess Diana and gave up entirely on doing any shots. Too many children, too little clothing and no way to tell which were parents among the many people standing around.
