This is a very cultural thing - in some, it's very rude; in others, it's a common and acceptable pastime. The mixed signals come from not knowing the difference, wherever you happen to be.

In Germany, overt people watching seems to be the norm. (Or was, in the 1970s. I don't know about now.) It meant absolutely nothing at all.

I was brought up, by my dad, to make eye contact, smile, and offer a hand for a nice, firm handshake - to everyone. Male, female, higher-ranking official - whatever. Didn't matter. But in Mexico, when I was 16 and quite attractive to the opposite sex, apparently, I was asked to STOP PLEASE RIGHT NOW by our tour guide, who said he was tired of running interference and playing bodyguard.

Oooookay. I had no idea why strange men were crossing the street to proposition me. After that, I almost dyed my hair black and started wearing a shawl like an old woman. (I didn't, but I was very close to doing so!)