So much great observations on street photography habits and techniques. I think it is all about attitude and this depends on how is our own character. I feel myself very identified with the OP, as suffering from anxiety also occurs to me whenever I try to do street photography. I am also a friendly person, or at least I think I am, curious to know people and I am not particularly shy. However I am kind of tall for the average in Southern Europe and somehow I might not be an unthreatening person to other people just because the way I physically look. I would say that if you don't feel comfortable my throwing your camera between strangers, it's just that street photography will never be your best field. But hey, that should not prevent you from taking some interesting picture from time to time. You may not catch people's soul as V. Meyer did (what a fascinating woman she should have been), but if you keep training your eye you may find some good opportunities to take a snap.
I am lucky to have a Ricoh GR II. Small size and noiseless click do help a lot. Be prepared to react quickly (auto ISO?, min shutter speed?, etc). Never stop smiling gently when doing it. Not too much, just slightly. Drive your attention to a different thing after the shot. Do not get too frustrated if you're incapable of shooting from the front. I am usually neither that brave. Try to compose the shot with the elements you have. Do not refuse to shoot even if everyone is giving your back to you. Try not to concentrate on street photography, but on just on photography. Eventually a street scene may occur. If you loose it, think about the things you should you've done. Do not blame yourself too much if one day you got nothing. It will come as long as you keep observing. I believe that below 50mm effective focal length is better. Sometimes it's about luck too. And character. I know a guy who shots always a K30 with the kit lens always at 18mm and he gets incredibly amazing stuff just because
the way he is.
These are some examples of shots made as a coward photographer. Not brilliant stuff but just to demonstrate that we can also get some shots too.