I can think of three such occurrences:
I bought some (kind of frumpy) shoes from Payless. They kind of looked like men's shoes. Later, I noticed a friend's wife was wearing those shoes. They looked more appropriate matched with her trousers than they would with a skirt (how I would have worn them normally).
I took a six-week sewing class at the local community college. I dressed pretty to the class each week. I wore a black and withe striped maxi skirt one night. The professor entered the room wearing the same skirt in gray and white stripes. That was awkward. I was thinner than her, but I think it looked better on her because she had womanly curves. I saw the realization on her face that we were wearing the same skirt. I tried to stay invisible in order to make it not be awkward for her in any way.
I was walking into the office and saw a woman wearing a dress that was very similar to one that I owned. We entered the building together and waited on an elevator together. When we both were in the elevator, I said, "I probably shouldn't say this, but I own that same dress." She smiled at me. I added, "I was interested to see how you styled it." She laughed and responded, "Well, you must have excellent tastes!" Then, I said "Good-bye," and got off on my floor. She said, "Have a good day!"