It really does depend on the circumstances, and your own demeanor. Hate to say it, but men in particular seem to set off the radar more than women photographers when taking candids, but then again, I know a number of men who excel at it. They always approach and ask - nicely - before they take the shot, explaining why they are doing it. Most parents will accept that, those that don't, go on to the next.
As a parent, it is just natural to be concerned about where the photos will be used these days. Unfortunately, there are reasons to be concerned.
I have had parents approach me after shots I've not asked about prior asking me where they will be posted, and if they want me to not do so, I'm happy to comply. You never know their particular circumstances, even when they are at a public event. I never want to create a fear of the camera in people, so it's best to comply instead of dig in.
I had a teenager at a high school football game I was working this season chase me down as I was leaving and ask if I had taken a photo of her. I had, and showed it to her, it was a good photo but I could see she was distressed about it, so I showed her as I deleted it. She thanked me and explained she was very paranoid about an ex-boyfriend that was stalking her, and she didn't want anything out on the web that might encourage him to comment or try to contact her at her new school. I had no problem with that.