How does EU "fight" that? By playing for the long run: freedom of movement, cultural exchange, freedom of business. In the long term this leads to a more liberal society, regardless of counter movements.
Does spain is included in your non-nationalistic western europe? A state where old fascist are still in charge in justice, police and army? Who cheeringly cracked down on catalonia who dared to organize a referendum on independence?
Or, well france. Who declared as a first move of presidency of EU to make french the standard working language of the EU?
Nationalism isn't restricted to eastern europe.
Which would likely be done by every country that respects rule of law and equal rights of its citizens.
https://en.m.wikipedia.org/wiki/Self-determination
Aside from that, the UK showed with scotland, how it can be done dealing with political issues, without involving the police. Because that is just in tradition of the fascist way.
Parts of states do not simply arrange independence referendums without approval from the central government. This would be “cracked down” in every single country on earth. It may well be that Catalonia deserve independence but it’s not exactly surprising or authoritarian of a central government to stop such attempts. Scotland doesn’t arrange an IndyRef without getting a nod from London.
UK says hi!