Dear Douthat, the church's struggles are not primarily left vs. right
On Monday, I laid out my cultural analysis of the Church, although only in passing. There is a definite authoritarian strain for many, and not just among the bishops and some of the priests. The people in the pews are quite willing to accept the authoritarian culture of the old Church. It works for people, especially the certainty. This is not necessarily a bad thing. There are others who are open to a more thoughtful (read libertarian) Christianity. The two can exist together in the same Communion line.
Some freer thinkers form sectarian groups, however a feature of sectarianism is sometimes separation. For others, it is serving on the parish social ministry. (some of whom are pro-life Republicans). Regardless, those who do charity are the ones who have treasure in Heaven. The hierarchs are more traditional in their belief, but they do engage.
Going back to the authoritarians, there is that danger of mixing their traditionalism with their Republicanism. You won't see many waving rainbow flags. You will see Rosaries. They are all united in a common belief in Christ. The people who simply belief in the belief of God, as Daniel Dennett puts it, have long since departed. So have many for whom authoritarianism did not work. They are spiritual, not religious - in other words, they are both recovering Catholics and Catholics in recovery. Even they still retain the grace of their Baptism. Faith, hope and love, especially love, does not leave them when they leave the Church.
And then there is sex, where all of these cultures are found, from the authoritarians to the nones. There are a few who will not use birth control on one end, while others who think abortion is not immoral (who are definitely not authoritarian). Among the priests, there are those who would have women ordained, some who are gay (not mutually exclusive), some who are happy as asexuals and those who are in the closet, especially to themselves. The last are those who should be both pitied and feared. The old rules will not help them, but if we do not help them the fate of the Church is dubious. It is in these times when the Holy Spirit comes to the rescue.
Note that I just released a revision of my book series of blog posts. Now I have to add this one and reload it onto Amazon (right after Monday's column). See https://www.amazon.com/dp/B08LTC18HL
One last thing: Napa Institute Catholics who want their brand of lay oversight are not libertarians. They are authoritarian capitalists. They buy obedience with money (rather than threatening to withhold the Sacraments). Real libertarians are few and far between in large organizations. That is kind of the point.