I find the only strangers who ever try to talk to me in public are the ones who want something. This means I'm always suspicious of people who approach me, and have an aversion to being seen as the same.
Your worries about being seen as the same are silly, people can usually tell whether you want something from them a few sentences in and after that a pleasant conversation is usually in progress. It's worth it to strike up conversations with randoms. On the elevator one time I had a fun talk with an optical engineer about detecting methane leakages with lasers and whether it had applications in space.
Similarly, I’ve experienced some extremely skeptical looks when I sit down next to a stranger my age on the bus and ask “how’s it going”. Some people here are very business-oriented, I guess: it ends up being less socially awkward if I open with something that’s on the surface more selfish: if I’m on the window seat when a stranger sits next to me it’s “which stop are you?” ... and then “I’m getting off just before that - I better take the outer seat” or “perfect, I’m riding until <xyz>”. Now I’ve broken the ice, in a way that’s more acceptable for whatever reason, I’ve had a minimal amount of interaction to guess if they’d prefer to talk or be left alone, and if talk, we both have opportunities for conversation-starters (whatcha doing at <xyz>).
I don’t know what to think of it: maybe I just overthink these interactions. But it’s been disappointing for me to finally start taking the initiative to speak with strangers only to find that 3/4s of them want nothing to do with it.
