Honestly, there’s some clickbait out there with that recommendation, but the only legitimate reason to put plastic bags on car mirrors is to keep ice from forming during an ice storm.
I’m sure you’ve spent chilly mornings scraping away snow and ice from your mirrors—I sure have. But by simply covering the mirrors with a plastic bag, you can prevent snow and ice from covering the mirrors!
Obviously, you wouldn’t do this while driving, but if you’re parked outside and know there’s going to be icy rain (and you don’t have heated mirrors), it’s a good trick.
When it comes to preventing car break-ins (by supposedly obscuring the view of your backseat from passersby), the advice is questionable. By putting the bags on your mirrors, you’d likely just attract more attention!