It's only weird if people think it's weird. If it's not weird to you then it's not weird. Who cares what the strangers think? You won't see them again anyway and if it happens enough then they'll stop thinking it's weird too. The best way to counter this "talking to strangers is weird" phenomenon is completely ignore the possibility the other person might think it's weird, and go talk to them. If you get good practice at it, they might think it's weird for half a second and then become completely comfortable talking to you.