Folks on opposite sides of the pond have caricatured ideas about each other, because their impressions are based on anecdotal media representations. Compounding that is the fact that “parties” are very different things in the US system versus the parliamentary system. Parties in Europe have a lot of control over who runs under their banner. American parties do not. If the Republican Party operated like European parties, where the leadership selects candidates, the 2016 candidate would have been Jeb Bush of Marco Rubio, not Trump. But in an objective analysis, the Republican Party is solidly to the left of the SVP:
https://www.nytimes.com/interactive/2019/06/26/opinion/sunda.... It’s on the right edge of the mass of European center-right parties. (I would argue that this analysis somewhat overstates how far right the Republican Party is. As the article notes: “The Republican platform does not include the same bigoted policies, and its score is pushed to the right because of its emphasis on traditional morality and a ‘national way of life.’” Americans are by far the most religious developed country. In France, arguing for the maintenance of traditional French social norms is something you can do in a secular framework. Under the analysis of this survey, that doesn’t count as right wing. But there is really no way to express that same idea in the American framework while leaving religion out of it. But in this analysis, that counts as right wing.)
I’ll add that Americans are in a different stage of the same overall trend we’re seeing in the developed world. Even right-wing platforms in France or Germany have never needed to call for adherence to traditional French or German values, because it was taken for granted. 80% of Germany is still ethnic Germans. Another 10% are other kinds of Europeans. In the United States in the United States only 60% is of European ancestry, and even among those people you’ve got a mix of British, Germans, Italians, Irish, etc. European countries aren’t really multi-cultural the way America is, so there is no need even for right wing parties to make culture an issues. French being the national language of France has overwhelming acceptance (90%+). There was never a reason for right wing parties to even bring it up. But in America, making English the national language is a right-wing talking point, because Americans don’t take it for granted.
But taking culture for granted is something that is rapidly changing in Europe. Le Pen got 30% in the last French election. Now she’s polling at 45% in a head-to-head with Macron. The dominant CDU in Germany is bleeding members to AfD. The new leader of the CDU is significantly further right than Merkel: she opposes abortion and gay marriage, and declared the 2015 acceptance of refugees as “a mistake” that they’ve “learnt from and won’t repeat.”