The DSA itself imposes EU-wide requirements on the “mitigation” of “illegal hate speech”, although it does not define the term. Section 35, 1(c). My amateur guess for how this would end up is that large European wide platforms will be expected to take down hate speech that is illegal anywhere in Europe, but I don’t think we have seen an example for certain. It’s possible this enforcement action will bring more certainty.

https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=celex%3A...

I think this is going to inevitably create more and more tension between EU and American contexts, because hate speech is affirmatively legal in the U.S., most recently ruled under Snyder v Phelps.