Not in the least. Dominionist and dispensationalist theology has had a huge influence on modern American evangelicals who in turn have a very significant influence on American politics.
I don't think anyone was suggesting that religion only influences the right-wing, but rather that dispensationalism and dominionism have a greater influence on politics than you're accounting for, and that those movements have a much greater influence on the right-wing than you're accounting for.
There is a growing movement within christianity that recognises this, and has thereby found a way to environmentalism along the right flank of politics. The pope is all in, and so are many protestant churches in Europe. It's mostly just US protestants/born-again reactionaries that continue to only read the unwritten parts of the bible that align with Ayn Rand.