Saying that a movement is modern because it originated in the modern period or in reaction to modernity isn’t the same as saying the movement’s content is modern.

You can speak of various conservative movements in narrow senses, but I’m talking about a big-picture view of history. In that view, absolute modernity is defined by the humanistic revolutions that were liberal in contrast to most ancient and medieval civilizational norms. So-called modern conservative movements, then, either agree or disagree with that essential humanism, or with absolute modernity as such.

That’s my big picture, and you can argue that I’m oversimplifying the premodern social norms, if you like. But pointing to how modern conservatism has evolved over the last century or two is neither here nor there, I think. I’d credit those developments to innovations in the rhetoric used to excuse the medieval effects of implementing conservative/anti-humanistic policies.