Greetings - It has been my experience that there are three kinds of persons in public as subjects. First, those who don't know their photo is being taken. Second, those who know their photo is being taken, and don't mind or seem to mind. Then there are those wo do not want their photo taken and will express it in one way or another. The first kind is no problem and can provide the best candids. The second kind is no problem except they may not be as candid as you want. The third kind is problematic. I for one respect their desire not to be photographed. However in public, under almost all circumstances, you have the right to photograph the unknowing, the knowing and those objecting. I usually ask and then as they go about their activities, you can get pretty good candids and even posed shots that are interesting. There are those here who feel that no permission is needed (and they are correct) and who upset those in the third group by not respecting their wishes. If the shot is worth bodily harm and/or the damage to equipment, go for it, because you will be in the right and they will be in the wrong. Photographing children can be quite sensitive. I never do that unless the circumstances would imply that there is no objection. If asked to delete a photo, I will, gladly. Others will absolutely not because it is their right. Only you can strike the balance that is best for you.
Cheers,
John