I ordered two LP's from Amazon at the same time. They both arrived the same day, one in a cardboard mailer the other in a plastic bag. The listing for each LP listed Amazon as the order fulfiller. Amazon has until now been great, but it appears those days are over.
Amazon Ships Records in Plastic Now
Used to be that they would ship albums in an Amazon box or sometimes even a proper record mailer. The box wasn't a good fit, but it provided protection. Now, they ship in plastic. Both of my albums seemed to arrive okay, although I haven't had the chance to play them yet - visually they look fine. The Prime is convenient, but this does it for me - I'm not buying any more albums from Amazon.