Pasting a copypasta is probably actually copyright infringement. Same with memes.

The thing about copyright is that it really only matters if you choose to enforce your protection. Presumably the owners of the copypasta don't care enough and the owners of the memes think it brings more popularity to the movie than any licensing costs they could possibly gain from selling the stills.

(Some memes may be considered transformative enough to be fair use, but some of them almost certainly are not.)

Video game streaming is a clear example of this. Almost certainly live-streaming or doing full gameplay videos are infringing the game owner's copyright. The work is often commercial, is often a replacement for the original (at least for some people) and very rarely transformative. But most game publishers think that it is worth it for the advertising. So they don't enforce their copyright. Many publishers will explicitly grant licenses for streaming their games. A few publishers will enforce their copyright and take down videos, they are likely well within their rights.

Tom Scott has a fairly good overview of basic copyright knowledge: https://www.youtube.com/watch?v=1Jwo5qc78QU

I don't know if I would say the internet is opposed to copyright. I think there is a lot of misunderstanding and a lot of not caring. If the average internet commenter posts a meme it is of such minuscule cost to the owner of that work that it doesn't make sense to go after them. So it sort of just happens. This makes people think that it is allowed, even if it probably isn't. Most people would probably also agree that this is morally ok. But I don't think that means that they are against copyright in general. I think if you asked most people. "Should I be allowed to download a CGP Grey video and reupload it for my own profit" they would say no. Probably similar for "Should I be allowed to sell cracked copies of Celeste for half price".