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Don't use a telephoto. It'll bring more attention to you and people will probably think you're a pedo. Just swallow your fear and keep taking photos of people, it'll get easier the more you do it. The best tip is to look beyond them as if you're taking a photo of the street or a landmark beyond them. If they ask directly, tell them you're new to the area (a tourist) or be honest and tell them what you do. Most people don't care, it's just rare to own a camera these days and it makes people suspicious more than a phone camera does.
Personally I use my Ricoh GR or Olympus XA2 on the streets and it serves me fine. They look like tourist p&s cameras and don't bring a lot of attention to me. You have to get really close though due to the wide angle.
