On an old episode of the "Rachael Ray" show, she said, " The consistency is weird to me… there's something about a shelf-stable egg that freaks me out."
Since it's shelf-stable, store-bought mayo can be stored safely at room temperature when sealed. While unopened, the additives, such as antioxidants, stop it from becoming rancid.
In contrast, homemade mayo prepared with fresh eggs and oil has to be refrigerated as soon as it's ready because it hasn't undergone commercial processing.