I don't blame GDPR for those pop-ups. I blame sleezy business models. Those businesses don't need to make those pop-ups so annoying, they are doing it on purpose. After awhile you'll recognize them and automatically open them in private/incognito mode

The only parts of the internet I haven't been able to access from the EU are US local and regional news sites who throw a 451 error because they are managed by immature people. If it bums you out that much, just check the page via archive.org. You'll see you're not missing much