Jon Mahoney has a forthcoming article, Protestant Christian Supremacy and Status Inequality, that is interesting, not so much because it is any good but because I suspect that it is an example of a genre of which we will likely see a great deal in the future. Mahoney says:
Protestant Christian identity confers status privileges; it correlates with opportunities to serve in public office, especially at the national level; it serves as the paradigm for religious identity against which other religious identities are compared and judged; it is a significant source of exclusionary immigration policy; and it renders white supremacy, patriarchy, and anti-LGBTQ prejudices and policies more impactful.
The argument for everything in this paragraph is rather handwavy. For instance, Mahoney notes that nearly half of all Presidents have been Episcopalian or Presbyterian, but gives no indication of how this establishes such a thing as "Protestant Christian identity"; he claims that Protestant Christian identity is "at the core of how many Americans imagine their nationality", but gives no particular reason why we should think so. Protestants are an extremely diverse group, by nature; he says nothing about how a Southern Baptist and an Episcopalian are supposed to have a single identity that would work in a plausibly causal way to do these things. At one point he tries to argue that court cases exhibit Protestant Christian bias by pointing to claims by Justice Scalia, who was famously not Protestant and on a court that famously has been tipping Catholic and Jewish for some time now. Such is par for the course; Mahoney is not actually doing serious analysis, but trying to do social philosophy with cartoon caricatures. This is, I say, something that seems to be increasingly common.
But the thing that really puzzles me is the practical upshot. Most of Mahoney's examples are not particularly great examples of what he claims, but we can find a case that one could very well interpret as "Protestant Christian supremacy", namely, the rise of government-funded schools in the United States. In at least many states, support for this move was due to fears about Catholic schools. Many local communities were largely Protestant, but Catholic schooling was expanding and also had a reputation for quality, much like it does today, and there were worries about how this put Protestants at disadvantage. This gave a great deal of impetus to supporters of public schools, and basically the schooling system we often got was a public school that accommodated Protestant practices but not Catholic or Jewish, or that accommodated the former directly but the latter only by special exemptions, or any number of minor variations on these. In addition, Blaine Amendments were passed and made part of state constitutions primarily in order to prevent state educational funds from flowing to Catholic schools. A general result is that Catholic (and other religious) schooling became more expensive, because Catholic schools had to compete with public schools that are funded out of vast tax revenues and because it creates a situation in which states can impose regulations on schools while both giving public schools additional aid to comply and denying any such aid to religious private schools, a large percentage of which are Catholic. All of this was done fairly explicitly in some parts of the country, you don't need to read between the lines, just look at the political campaigns, legislative debates, and other various shenanigans associated with the development of the public school system. It was by no means the only factor, but saving Protestant America was definitely one factor.
So let us assume for the sake of argument that this all gives us a good reason to attribute the public school system to "Protestant Christian supremacy". And, whether one wishes to attribute it to "Protestant Christian supremacy" or not, and despite the fact that our culture is much less Protestant than it used to be, it's pretty clear that the ethics, view of society, etc., that is taught in a typical public school is even today much closer to liberal Protestantism than to Catholicism. What then? What are we supposed to do with this? Are we to conclude that the public school system needs to be dismantled, so that we return to a mix of homeschooling, apprenticeship, and schoolhouses supported by sectarian or community associations? Mahoney gives us no answers -- the entire practical advice he gives about this supposed problem is that we need to make it part of the discussion. So we've made it part of the discussion. What then?
Public schools are not explicitly Protestant; as time has gone by, they have slowly done a better job at accommodating Catholics, or Mormons, or Jews, or Muslims, or Jehovah's Witnesses, or what have you. There are communities that are not very Protestant at all, being dominantly Catholic or Mormon, that use the public school system without any problem. Protestants did use public schools as an indirect way to cause problems for Catholics (and explicitly), but it's not as if Catholics have received no benefits from the existence of public schools. So one could argue that perhaps the inequality is not severe enough given the overall benefits to require dismantling the whole thing. But then we'd still need to know what to do about it. What possible practical policy could you implement to get you the result that the practices and curricula of your public schools were at some hypothetical equilibrium point in the midst of all the possible sects in the whole nation, giving none of them any advantage over the others?
Perhaps, though, this is just tied to my difficulties with understanding how the egalitarianism is supposed to work at all. We seem to be required to have a democratic society in which the direction of the society is determined neither by consensus (since practically speaking we can only very rarely get that) nor by majority (since this creates biases in favor of the majority) nor by the more politically active demographics (since this creates biases in favor of the politically active subpopulations) at all. I don't even know what that would be. Even in a very smoothly functioning society, in which majorities and active subpopulations make extensive concessions to minorities and less active subpopulations, the tenor of the society is still going to have majority-aligned biases and active-subpopulation-aligned biases, and you'll still get inertia in which society still functions in a groove laid down by a no-longer-majority or no-longer-active group because it's a lot of work and agony to make new grooves all the time. These discussions always want to talk about the case-by-case inequalities; but they propose alleged explanatory factors that are necessarily society-wide, without ever telling us what a society without any such factors would look like.
One worries, indeed, that the purpose of a concept like "Protestant Christian supremacy" is not to give any explanation at all, but to give a justification for attacking Protestants. In practice it sometimes seems to work that way. But in this case, perhaps not. I've noted before that, while individual academics can be creative, academia gets its results not by creativity but by being a combinatorial machine that runs through huge numbers of variations of ideas in both parallel and series. Fashion and precedent feed in the inputs, and the whole system just explores different variations on them by going through the possible combinations. 'White supremacy' has had some fashionable purchase, so it's perhaps inevitable that the combinatorial wheels will roll, and we get endless explorations of an 'X supremacy' sort. Perhaps someone has somewhere started writing a paper on right-handed supremacy. Eventually you might even find some excellent ideas. But you also get a lot of unhelpful things.