Great advice Dilbert, very true.
For me, I've tried about every approach to deal with strangers. For the longest time, I would feel obligated to do as everyone else did, which was try to be open and friendly (smiles, forced eye contact). It wasn't until later that I realized just how scripted my social life was.
I had no feelings for people - how they felt, what they thought, how they see and do things in life, what they had in common with me, etc. I grew up witnessing people in conversation, saying things like, "How are you, is that a southern accent, I like your truck, looks like it might rain later...." and so on. I felt like I needed to do those things if I was going to claim to be a human. What I didn't realize was the millions of dead end conversations I had clocked over the years without any emotional satisfaction gained - I was simply mimicking those closest to me.
Now, I actually know what a sense of satisfaction feels like when I am in public because I don't feel guilty for how I act or look to other people. If I am walking the isles of a supermarket and my mind decides that it wants to loft away to outline a chapter in my book, I let it - and I don't concern myself with the lack of attention that I'm giving to approaching strangers...
By-the-way, strangers passing by may look at you in whatever way they look at you. Just know that after they walk by, they won't be thinking about you because they are too busy solving the problems to their own daily life. You are no different to that stranger than the person who is walking behind you and in front of you...
We all are different as individuals... but we are alike as humans. All 6.8 billion of us.