I think it's already been articulated that CN is an abused term, so you're not sure who is or is not a true CN. Our current Speaker of the House was accused of being a CN because he dared to claim that all Nations are ultimately under the control of God and that laws need to be judged by that standard. From a political theory standpoint, however, he's certainly not advocating for an Establishmetarian form of government.
It's probably good to read a book about the branches in American Conservatism and other "fly-bys" around various political theries.
These two books are worth reading:
The latter of the two is really good at setting the stage for the divide between notionally "conservative" visions for government. I put "conservative" in quotes because a lot of what would be considered classically liberal or even libertarian ideas seem "conservative" to a society that governs by sentiment and allows all sorts of crazy ideas.
David French, for instance, seems like a conservative to Progressives, but he is a classic liberal who is devoted to ideas of evident human reason about liberties in theory. This is why he'll defend the idea that a "conservative" should protect the rights of gay people to marry or to not interfere with Drag Queen Story hour. It's a form of Jeffersonian liberty that men should be free to do anything that doesn't "harm" another.
The kind of conservatism practiced in America was what one might call a form of Christian Republicanism. It conceived of the citizen exercising constraint in the exercise of liberty and that the State had the right to constrain liberty for the public good. It had no qualms in enforcing Sabbath laws in the States or even passing laws that were in accordance with Biblical principles. Some States even curtailed or outlawed harmful religious sects.
I don't have time to really write out what I'm trying to fully articulate but, suffice to say, there are many professed Christians who would describe the vision prescribed by Yoram Hazony in
Conservatism: A Rediscovery as "Christian Nationalism," but he's not a Christian. He's an Orthodox Jew. In a public forum, he even argued that America needed Protestants to recover this vision for governance because the Anglo-Christian conception of liberty is what made America so distinctive as a Republic that ensured liberty for so long. In other words, he
wants to live in a country where the Laws are informed by a Christian conception of liberty and not the classic liberal notion that is best illustrated by the disasters in France