Records in particular would get majorly looked over in customs, stuff from Europe to the US especially. I don’t know what they were looking for (Acid? What can you fit in an LP/CD case?) but I couldn’t get anything with shrink on it still for most of the 90s.

it seems I have internet again, heh

I confirm for the Macross and Ghibli boxsets, discs have bags
it is true shrink wrapping was more common for early releases, esp. music titles. je280 already mentioned VIDEO ARTS titles
I have a bunch of early music titles (Pink Lady, Kyon, C. Moritaka) and all are shrinkwrapped

However Conan and BBC were quite late boxsets and the discs have no bags, so it really depends, I guess

on a related note
that guide from mimy is very helpful, I'll give it a try
however He mentions to not use it on a simple sheet of paper, or it'd get damaged
I wonder how could you remove foxing from, say, a paper booklet
or a stronger plasticky booklet
like this
https://page.auctions.yahoo.co.jp/jp/auction/o424768943
if you scroll down the pics, you will see the booklet has some major foxing on the top

Do it at your own risk but just don't let a blob sit on plain paper, it will wrinkle a little and do a test.