If DPP is a Nazi party, the Republicans are also a Nazi party. The DPP is actually more moderate than Trump: compare their stances on Syrian refugees, for example. This means the welfare state-less America is heading towards ~45%, so Denmark is doing pretty well.
That's a bit of a facile answer, though I thought I'd point it out. The real answer is that no, the welfare state isn't the most important factor here, although it can ameliorate. No amount of increased welfare from the state can make up for flatlining earnings; no amount of benefits really makes up for the indignity of unemployment and the loss of stature; and some pity from the cultural elite doesn't make up for the fact that the professionalization of politics across Western countries has removed the voice of the working class. The cause of rising far-right sentiment is this stagnation and feeling of being left behind and ignored; the losers of economic liberalism and globalization. Tackling it means more than just having more generous unemployment provisions; it means bringing back jobs, retraining people whose livelihoods have fallen by the wayside, trying to increase wages, and so on.
You go up to the north Welsh valleys and those places are sad. They were killed in 1984 by Mrs. Thatcher and the world didn't even bother with a funeral. Unemployment is crossgenerational and endemic. Towns are crumbling. Schools barely have the resources they need to function. Anyone who can make it gets out as fast as they can. There's no jobs. There's no hope. These were and to an extent are Labour strongholds. But they don't recognize the Labour Party; it's full of those ivory tower folk now, who don't represent them and even worse, don't make the effort to understand them. These areas were Brexit landslides. It's the same story in France - the Front National does best in places that in the 1980s were Socialist bastions. It's the same story in Germany - AfD does best in the East! And, of course, it's the same story in America. Trump is the candidate of rurality and rust.
Plus ça change.