“Why was she in Target, especially the laundry detergent aisle, in the first place? I seriously doubt that she does her own laundry.”
She was playing a game. She wanted to know if she walked out in a disguise among the great unwashed if she would be recognized. She was, in effect, playing Halloween.
Considering that the SS agents made all the customers leave and put in 'actors' to be pretend shoppers, and that an entire film crew along with SS agents dressed as customers followed her around the store, I doubt if there was one single person inside the store (or outside) who wasn't aware she was there.