I have some sympathy for a teacher in that situation. If someone takes a picture of her students and publishes it, it can hurt them or her depending on context. That risk disappears if the picture disappears.
And I do think it's generally OK to ask people not to exercise their rights as a favor: I might ask a neighbor to move their car to free up a legally occupied parking spot for a disabled relative; someone with children might ask adults not to use legal but racist or misogynist language in front of their kids.
I agree it's a slippery slope, especially if she's a public school teacher and bound by your countries' free speech, etc., laws (and more likely to have the advantage if she calls police).
There was a time when you could have a very large event, e.g. an 'illegal rave' and, despite hundreds attending, there would be no evidence of the event ever happened unless someone was a keen photographer and happened to attend. Back then people who took a lot of photos were sort of social misfits that could not enjoy the 'now' properly, as if they had to freeze in time some definitive proof that they once had fun. The taking pictures took them out of being a participant to being an observer. Cameras on phones has blurred that distinction, it is okay to take pictures of stuff. Of people, it is how you do it.
I think that the actual technical parts of photography and getting things like timing right can be done using animals as test subjects. Birds fly away, big animals like cows can make unwelcome advances. You can snap away knowing that no animal is going to be offended. Then take photos the same way but nearer to town. Keep going and then you can take pictures of people in the city without feeling so awkward about it as you are used to people seeing you taking photos and are happy with that part of it. Also, with countryside snaps it is clear that the subject is the view rather than those people walking through the field. Those people are assumed to be in shot rather than the subject. It is all easy in the world where everyone has a camera.
And repeat that process when traveling, with added emphasis on cultural aspects.
But, if we went ahead and were timid about pictures in this place or that place, no photojournalism would take place, if we took it to extreme. I give photography a pass when it comes to cultural awareness. Otherwise we'd have people say things like "Robert Frank had no right to portray "The Americans" the way he did, he wasn't American and didn't understand us". Of course, have personal awareness --some people are weary of strangers taking their pictures --say Bruce Gilden taking pictures of the Yakuza in Japan.
On the other hand, be decent and don't take gratuitous pictures just for the yucks (someone in very embarrassing/compromising position that really don't add anything --a drunk/homeless in the street in their vomit, for example.
Here in Norway it is allowed to take photos in public of groups of people without asking but it is not allowed to single out a person in specific and take their photo without permission. I think cropping a photo to produce a portrait would also fall under the latter btw.
So yes, it's absolutely important to be aware of local laws.
To expand on that, you should do this even when travelling to another state in most countries. In the US for example, Arkansas nearly outlawed street photography: https://petapixel.com/2015/03/31/arkansas-privacy-bill-vetoe...
I would never advise the use of a zoom or telephoto on the street.
Hesitation and fear are the number one enemies of new street photographers. The reality of it is you can shoot just fine and not worry about it, but that only comes with time and experience.
Another part of it is learning to read the subtleties of the atmosphere and your potential subjects to know when and when not to take a photo. Some people very obviously should not be photographed, some you should ask permission, most you can just fire away. These days I don't even think about it unless the picture I want is quickly approaching Bruce Gilden levels of in-your-face shooting, which I rarely do.
Street is one of the most difficult forms of photography even for the experienced photographer. Adding the fear on top of it really hinders people.
