Firstly times have changed.
We all acknowledge that and HCB's day was different. Most people didn't even own cameras then. Having someone care enough to take your picture may have been a cool novelty.
It was still illegal to take a picture of someone (unless you worked for a newpaper/news publication) and publish it without their permission making money off it without a photo release . At least it was a gray area.
But times have changed, values have changed, as people have noted, the 24 hour news cycle has learned that fear is a great ratings boost, so lets keep them scared of everything.
So that's the world we live in and if we want to do street photography we have to adapt.
Personally when I did it, I would size up my shots with my camera pointed away and at the last second move it, take the shot and move it back. Using a reflex camera the mirror slap would attract attention but the subject would look at me and I'd be looking like I shot something else.
If the subject was looking at me when I took it and acted offended I'd simply go up and say that I was a photographer and that I loved to capture street scenes and give them my card. If they wanted to contact me they could and I'd send them a picture. Nobody ever did.
So I guess the moral of the story is, it's not 1940, do what you want but be respectful and take all the damn pictures you want.