I agree that it could get out of hand. We'll have to wait and see how it turns out. Since this is an EU law I wonder if it applies to content hosted on EU servers only, or any content that shows up in their users' results.
I suspect that Google and Facebook will not offer country specific blocklists like they do for Nazi content in Germany. If Hungary bans LGBTQIA content, it'll disappear in France. Europe can then have an argument about how they "really really not really" believe in free speech.
EU law applies to companies which operate in the EU.