As to LDS, my experience is they seem to like to go up and talk to people in public a lot now. Perhaps they feel it is less threatening.
Several times in my neighborhood park I have had them come up. Last couple times it has been 2 young women each time (they have to be older to go as women). Typically they have more to talk about when they leave than when they met me.
They also seem to be a bit naive and unworldly. Hard to imagine today.But, typically, I let no one just walk up to me... it's not that type of world any more, big city or little.