Realistically, the print edition is out and done. But I'm sure they'll add a photo credit to the story online.
Try to reach the photo editor if the paper has one. They'll be more sympathetic since they'll be from a photography background and work with photographers. I'd be nice (and include a link to your work/portfolio). It's actually a good way to come to their attention.
So there are two separate but related things:
1 Your behavior when taking photos.
2 Publishing these photos in public places like Instagram.
Sounds like it is more the second one. I agree with P5_Tempname19 that the answer depends on how you portray them. I think you should also consider the situation they are in (what kind of activity). Even if you can photograph a children's sporting event legally (and often you can't) without permission it is not going to be a good idea. A parent and child walking down the street - probably fine.
Also consider if the people are in a vulnerable position or situation. A disabled person struggling to navigate a city not set up for them, or a homeless person who doesn't have anyplace else to be except on the street. A child crying because their parent has been hurt. Of course that doesn't mean you should not take photos of these kinds of people. There are also important stories to tell there. But you should be extra careful to think about their dignity when sharing these photos publicly.
Asking for permission is always good, but I know is not always practical.
If you feel uncomfortable about a particular photo I think a good exercise is to write a small, maybe two sentence, justification for yourself. It forces you to think through the competing principles involved.