I do not make eye contact with anybody on the street. The reason why is I’m usually deep in thought and not in the mood to connect with a stranger. If I am attracted to a person, I might let my guard down some. But it’s not like running into somebody at work, or at a store or whatever.
I’ll allow myself the luxury of looking at an attractive woman on the street, but I’ll never actually approach. If they grant me eye contact then it would have to be some amazing contact for me to do anything other than smile and keep walking.
People on the street come in two flavors. Those trying to get somewhere and those who aren’t trying to get anywhere. In the case of the former, they are not interested in socially interacting with you, in the latter, you are not going to get much from interacting from them, unless having them ask you for money counts as fulfilling. Personally I don’t.