Everybody is completely and 100% against the copyright law.
There is a huge difference between the two from my point of view:
GDPR is not a law about "The Internet", it is a law about company records. It applies to Google, but it also applies to the Pakistani food stand on the corner. It affects Google a lot more, sure. I support the concept that a company does not have some inherent right to be a steward of my personal data without my explicit consent. GDPR is also easy enough for even tiny startups to comply with, and is significantly easier for small companies than large ones. It does not create a large barrier to entry for new startups or a rift between the existing small and large companies.
The copyright law, however, is a law about The Internet. It controls how businesses interact with the internet. It sets _technical_ restrictions on how they can do so. It sets technical restrictions that are probably not even feasible, at that. It absolutely does create a huge barrier to entry for small companies, and could possibly enshrine the existing tech giants into de-facto monopolies (I mean, if they aren't already...)
The copyright directive is horrible enough on its own. I don't see why everyone is in a rush to pull in mentions of GDPR to make it seem "worse". For a lot of us, it weakens the argument instead of strengthening it. Not everyone likes GDPR, obviously, but we can _all_ agree that the copyright law is garbage.