From his perspective, I don't think there'd be any disconnect between the two views: after all, if the American workers don't want to work for a market price, the Chinese laborers should certainly be allowed to. I actually see a lot of overlap between his views and the views explored in the neoreactionary thread.
Well, okay, I see what you're saying re: how Beecher saw things, although I just wanted to point out that, IOTL, as far as it can be known by us, a good number of the anti-immigration people in general(and the vast majority of outright nativists), in this country were also anti-labor; Beecher's anti-labor activism and seemingly pro-immigration views make for interesting reading(I could see him in a Turtledove novel, TBH), but were n't exactly universal; from what can be seen, pro-labor and (non-nativist) anti-immigration views were actually rather more common.
So, yes, I'd say some real opportunities were missed. what might have been, what could have been. Religious leaders all too seldom provided real world leadership.
This. A thousand friggin' times, this.

I think we can fulfill this challenge without resorting to changing doctrine. There are plenty of democrats(leftists) in congress now who identify with their respective religion. Jimmy Carter for instance was a born-again christian and extremely devout but he was and is today no where near considered a "Christian President". I argue its a framing. I think the best bet would make either the early socialist parties have a specific religious bent so that when they are borken up it isn't because they are "Godless Commies" and then they all go and join "good parties" or better yet have Christian democrats become prominent during the 10's-40's.
I can see this.
I will say if there is a religious right AND left we're going to get some screwy interpretations of left and right.....I can see the right being comfortable with immigration and Muslims, with the left being Nativist, but also accepting of Gays. In short the social issues will be distributed weirdly alongside the new economic frame.
Well, I dunno. But before I go in depth with my response.....do keep in mind, by the way, that not all people who advocated for immigration restrictions were necessarily out and out nativists; nativism was very much a mostly right-wing phenomenon(and many of the right-wing nativists were also quite anti-labor).....whereas it was quite rare on the left.
Anyway, here's my take: as for the right; I do believe that you could indeed get some of the
moderate right-wingers to at least tolerate more immigration and perhaps even become accepting of Muslims(or at least those who assimilate enough, anyway)....although I can't see the latter happening until about 1950, though; and the far-right isn't likely to budge much on either issue(and may possibly double down on their extremism at some point).
Can't see nativism gaining any
significant traction on the left, TBH; as I pointed out, nativism had been a right-wing philosophy, and, I'll add, for a good reason; the very phenomenon of immigration represented a change in American culture as a whole.....and a change that some felt threatened their way of life....or worse. The left, being naturally progressive, weren't so inclined to go that far(mostly).
With that said, though, the left did indeed have their own reasons for limiting immigration, but not nearly so much out of fears of "Papism", etc., as it really was about protecting, and advancing, labor rights; they didn't really care so much about where these immigrants were from, as they did making sure these new arrivals couldn't be manipulated by industry barons and their flunkies.
With that said, though, it's possible that some disaffected leftists may break off and form their own nativist movement at some point; these folks could form a "Third Way" type of organization, perhaps.