I have been shopping with my bicycle for ..... almost 40 years? If the OP is getting those kinds of reactions .... I don't know. I have showed up at stores soaked in sweat, wearing spandex or sometimes an oversized T-shirt dripping sweat over it .... I have shopped on days when i haven't washed my hair but should have, or when I needed a cup of coffee to face the world ... but had to go to the store to buy a bag of coffee. I have gione in sneakers, sandals, and cycling shos with road cleats.

Never got the reactions the OP claims he gets.

And I am at my best, ugly to an almost offensive degree. So I don't know what the OP is doing wrong ... I suggest he is imagining too much and should stick closer to reality.