IP law is not a natural right. It's been encoded into existence by laws. The GDPR is encoding new rights into law in regard with personal data.
I don't see a way to declare one bad and not the other unless you're just saying that new things are bad.
Additionally the terms of websites can say whatever they want but it doesn't mean they are legally defensible. I could put into my terms "by finishing this sentence you agree to be enslaved by Lovich LLC" but that doesn't make it happen
Yes, with some exceptions for actual copyright and the like.
>Do you not believe in any IP law?
IP law, yes, but I don't feel a user's entries into a website automatically qualify as IP owned by the user. The terms of many websites actually say that whatever you upload to them is owned by the website, unless a prior IP applied to it. I've only ever heard the claim that your name et al. are your inherent IP from "Sovereign Citizens" before.