If you want to call it right-wing, globalist classical liberalism/globalist libertarianism/neoliberalism checks the box too though it's hard to
per se call it right wing given how it tends to be socially liberal, not care much for tradition, and undermine established social and political hierarchies.
Dismantle regulatory systems of economic oppression that keep peoples apart. Free movement of goods, services, capital, and labor. The problem is that the process of exporting it by force tends to undermine it at home (ergo national security tends to be a big justification for undermining the free movement of all four of those things).
Good examples, I wonder if it would be plausible to unite them in some sort of international anti-secularist holy (or rather unholy) alliance, sort of like the attempts for collaboration between the Nation of Islam and Neo-Nazis.
Also, what would be the Protestant equivalent?
I don't see why a protestant faction couldn't operate the same way as islamism or transnational catholicism. If it's a high church protestantism, then copy-paste the catholicism example. If it's low-church, it'd be something like salafism perhaps.