Well, the mArkets and capitalism aren't all that defines a right-winger. Right-wingers are often nationalists who dislike the idea of selling of to foreigners and they're often pro-(native) business, unlike left-wingers who often don't see much of a distinction between home-grown and foreign business. That's who historically conservatives in pretty much all Western countries were hyper protectionist, and abruptly stopped when it became less profitable to be protectionist. But the Trump agenda is part of that lingering American conservative Protectionist mentality. (And in some part a lot of populist rightists in Europe nowadays are also this way). There are a few other countries where this sort of mentality predominates - the conservative LDP in Japan being ardent protectionists for obvious reasons. Indeed quite a lot of East Asian conservatives are traditional enough to still embrace protectionism.
I consider being anti fre-trade a more conservative perspective myself, although left-wingers can easily reappropriate
In the United States, free trade is generally more supported by Republicans and conservatives.
NAFTA's voting for example shows that the majority of Republicans supported the bill whereas a majority of Democrats opposed it:
https://www.govtrack.us/congress/votes/103-1993/h575You're also seeing more opposition from liberals and progressives against Obama's TPP agreement than from the Republicans.
The ironic thing is that Democratic Presidents seem to support these agreements (Clinton, Obama, probably Hillary too) yet Democratic Congressmen oppose them.