Academia!
Once upon a time, sectarian divisions mattered. I just had some students read Neal Stephenson and Nicole Galland's The Rise and Fall of D.O.D.O., because I can. Good book. In it, a 16th Century Irish witch living in London is unable to accept the notion of a future in which the Catholic-Protestant division ceases to be the central division between everything, and yet... here we are. It doesn't really define much of anything anymore. What does? "Religiosity." Lousy word, but it refers to the centrality of religion in your life. We measure it with variables like the frequency with which you attend services. As recently as a few decades ago, the Catholic-Protestant division predicted a lot about your politics, so the choice of denomination for something like a chaplain was a real statement. Today? Eh. Not as much. There is variation within any denomination, but the real thing is religiosity. People who are more religious are more Republican.
In 2016, according to National Election Studies survey data (yup, the same survey I always reference), those who claimed* to attend religious services every week voted for Trump over Clinton by a margin of 2 to 1-- 63% to 31.1%. Among those who say they never attend services? Clinton won their votes by 77.7% to 19.4%.
Why the difference? There is a lot here, ranging from group identification to the issue positions associated with strong religious beliefs (e.g. opposition to abortion and gay marriage) to Republicans' strategic choices. At the end of the day, though, religious people are much more likely to identify as Republican, leading to oddities like evangelicals embracing Donald Trump.
And yet, that relationship between religiosity and partisanship is strong enough that Republicans in Congress really aren't accustomed to having preachers say liberal-sounding stuff. The current pope, when he isn't busy running his child molestation ring, occasionally makes liberals happy with similar statements to Conroy, but part of the closing of the Catholic-Protestant divide in American politics has been a focus on abortion and gay marriage within Catholicism, and that's the point here. There have been a couple of Catholic chaplains, but changes in the structure of the political and religious coalitions have reduced the frequency with which conservatives have their beliefs challenged in religious services.
So, bye-bye Conroy.
*Yes, a bunch of these people are lying, but that's not the important point from a social scientific perspective. The question is whether or not they are more religious than those who admit they don't go to church. Look at the data. Something big is going on here.