Can’t speak for the US.
Europe isn’t really leaning conservative, though. It’s leaning nationalist-populist.
You have the prime right-wing nationalist-populists in FPÖ (Austria), DPP (Denmark), FN (France), GD (Greece), PVV (Netherlands), SD (Sweden), UKIP (Great Britain), SVP (Switzerland), FRP (Norway) and so on.
Some of these parties are quite different from the others. Most of what they have in common is:
- Euroscepticism
- Nationalism
- Populism
- Ethno-centrism
- Anti-elitism
A lot of them throw in laissez-faire capitalism for good measure.
When I say Europe isn’t leaning conservative but nationalist-populist, what I mean is that these parties have grown up in addition to the existing national conservative parties and movements.
For instance, in Norway the current government consists of Høyre and FRP. Høyre got about 30-35% of the votes, as usual. It’s one of the two big parties in Norway and is a traditional, conservative socialist-democratic party. They’re for lower taxes on business, smaller government, globalism, individualism, bla bla bla.
FRP* is further right still and has capitalized on the uptick in nationalist populist sentiment to aquire about 10-15% of the votes in the last election. They’re the ones agitating for closed borders, ethno-centric immigration, cultural identity, islamophobia, climate change denial, etc.
It’s kind of like how the Tea Party movement pulled the Republican party in the US further right. They’re not really conservative, they’re almost strictly reactionary, but they appeared like a lead weight on the far right of the scale and so they’re tipping the balance. (The left got the gormless Greens instead.)
(* FRP in Norway is one of the more-grown-up versions of this phenomenon, it’s been around for a while. This is the first period they’ve been in power though and their usual combat rhetoric has grown notable in its’ absence. They’re not governing well - where they’re not grossly irresponsible, they’re grossly hypocritical - but largely they’re being held by the ear by the conservative party. Still, it’s within the error bars and pulling their claws like this is an argument for integration into the political system instead of exclusion like SD in Sweden. )