This seems to be the nature of things, we rebel against or parents, and mature and change, our children rebel against us, ...

Rebelling against the rebels?

How apt. :-)

I think it's normal. We now live in a world were liberalism is being shoved down our throats at all levels (mass media, education, ...). Young people are rebels by nature, so now, young people are moving to the right, especially in Europe.

What I mean to say is that this is not the result of US puritanism moving to Europe. Instead, I think it's a natural, homegrown trend, unrelated to religious sentiments.

Left/right is a seating arrangement, literally as well as metaphorically.

Free-market/command-economy is different axis to dynamic/conservative is a different axis to populist/evidence-based is a different axis to moralist/libertarian.

If you just tried to transplant the UK’s Conservative, Labour, Liberal Democrat, SNP or Green parties to the USA, they not only would be unelectable “socialists” for supporting the NHS, but also all support policies the USA considers unconstitutional (variously: ‘guns are bad’, ‘censor more’, ‘the Queen should disolve the government every so often’).

Likewise, the UK’s Labour Party is currently wobbling on the left side of the UK’s Overton Window, despite being a moderate centerist by the standards of several EU nations.