The West does not currently have much of a problem with violent separatism. Maybe someone got into a bar fight over Catalan independence or Brexit, but all recent conflicts I'm aware of were relatively peaceful. If you compare this to the situation in Northern Ireland, I'd say things have gotten much better.
yougoslavian people will beg to differ. Civil war in a european country leading to the partition of the country into multiple states based on ethnic and religious criteria happened in europe just 25 years ago.
I have a slightly different perspective on what counts as "recent", most likely because I am younger than that. I also looked up the Troubles for my previous comment; apparently they officially ended in 1998, which is even more recent. Take my comment as referring to the last 20ish years when I talk about things getting better.
One might argue that Yugoslavia, then recently emerged from decades of dictatorship and still a communist Eastern European country, was not part of the ideological West at that time.