"The social consensus tells people that if someone talks to them in that situation out of the blue they are either mad or bad!"

This is what some would call "a limiting belief" and I used to feel this way. Every interaction is between the two people in it and it is a mix of what both people bring to it. There is a lot of communication happening with body language and tonality. I find when I feel clear, confident, and good--others feel this in my presence. By bringing this energy into the interaction (even in a normally non-social situation), comfort/safety is easy to establish, and going further isn't difficult.

Here is another way of thinking about new meetings: "I'm a great person, who wouldn't want to know me?" now when you're meeting people instead of fearing that they'll think you're "mad" or "bad" you can think "I'm doing this person a favor by meeting them". And if you really are a great person then this statement is absolutely true.

Here is why I care enough to write a long comment--when I was doing what the OP is doing, I felt awkward about it and felt like it was a secret, primarily because I was tired of hearing things like what you're saying. I'm glad I managed to avoid these kinds of messages and just push forward.