I don't know why, but I don't have any trouble to speak of when photographing people on the street. Maybe location has something to do with it (I'm located in the midwest - "flyover land").
Perhaps in a big city, people can be more confrontational or aggressive. But I do recall reading that some people say that in New York City, people will see a street photographer photographing them and just ignore him/her because they are busy and in a hurry.
I just go out and photograph people - I have had people ask why but they are okay with it when I explain what & why I'm photographing. It could be that if a photographer is at ease and not acting nervous or jumpy, their subjects are put at ease by their demeanor. I would say that 95% of the time if I ask to photograph someone, they say yes - although probably 90% or more of the time I don't ask and just shoot as I want to.
I always carry some of my B&W work prints of my street photography to show people if they ask questions, and some of my postcards with my contact information, an image and my website address. When I show the workprints and give the person a postcard, this seems to establish that I'm a "legitimate" photographer and not some weird person who is up to no good.
The main thing in my opinion is to establish the fact in your own mind that you are doing nothing wrong, unlawful or immoral in doing street photography. This conviction will put you at ease and allow you to project a demeanor of relaxed, quiet professionalism.
When I photograph on the streets, I use a 28mm lens on a 35mm camera and generally shoot in the arm's length to eight feet or so distance range from my subjects. Arm's length works well in a more crowded area such as a farmer's market, street fair, outdoor festival or county fair.
If you want to photograph at arm's length, ease up to your subject and look thru your viewfinder at something other than your subject. Look thru your viewfinder, moving the camera around slowly as if searching or a subject to shoot. Your intended subject will eventually come to accept your presence and ignore you.
This is when you can slowly move your camera to include them in the viewfinder and make a few photos of them. After you shoot a few photos, keep your camera to your eye and look away from your subject.
Return to them after a short time (perhaps 20-30 seconds) and make a few more images of them. This seems to work for me without alarming or offending the subject(s) of my photos.
Give this technique a try and let us know how it works for you.