I don't think people would be ok with that at all. It would be a drastic overarching policy and not something any democratic EU member state aims to achieve.
Just because Europeans subscribe to a different notion of freedom of speech that doesn't mean that people want siloed and separated social media (except natural language barriers which do that automatically for most). Some probably want a "family friendly" internet but that's not unique to Europe.
Speaking from (my) German perspective it's important to realize that the national trauma of the Nazi and (Eastern German) Communist/Socialist regimes is embedded deeply into the foundations of society (e.g. even most far right extremist pay lip service to not be associated with the OG Nazis). A vast majority of people agree that the wish for society to not fall under one of those regimes again outweighs the freedom of individuals to advocate for violent far right/left causes and the abolishment of democracy.
A similar (though much weaker and more controversial) sentiment exists when it comes to celebrating crimes again humanity.
Anything beyond that is highly controversial and was/is a topic of many debates and political fights.