Just say no. Support local record stores. Even if they're in another state. Many of them offer shipping and many are on Discogs.
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.