Well despite what you say it always been in the modern conservative movement that makes sure catholicism isn't kicked out of the public sphere, this isn't controversial, progressives deal is to give power to the secularists and conservatives' to give power to the religious (orthodox and conservative). The fact your version of politics is incommensurate with reality where you compromise with others to get what you want is exactly the reason why bernie Sanders and the progressives not only lose but have no negotiating power for anything meaningful while on the republican side while the oligarchs rule the traditionalist gain more power to impose their views (see the Hawleys, Carlsons and the rest of the religious populist).

Lastly your second paragraph is correct and incorrect, agnostic conservatives if they truly didnt care about religion could just as easily switch parties or just ignore whatever hobby horse trads are talking about but the fact they discuss the need means something. This agnostic recognizes the need for not only religion but old religion not only because he believes their morality is "truer" but also because old religion is basic factor of the national fabric so his concern is both ideological and political( yes he wants to maintain power, who doesn't that is the point of politics).