Schenkerian analysis is, broadly speaking, a rediscovery and popularization of melodic reduction approaches that were well known to composers and performers in the 18th century. There's very little that's specifically American about it, let alone German. See Nicholas Baragwanath, The Solfeggio Tradition: A Forgotten Art of Melody in the Long Eighteenth Century. And of course, Schenker's "imaginary continuo" is readily understood as a popularization of historical partimento (and closely comparable approaches such as the so-called Partitura known from German sources).

It's true though that Schenker's treatises included plenty of political asides of such an extreme chauvistic character that to call them "quite right wing" is a huge understatement. (It's also true that, as scholarly research has pointed out in recent years, he seems to have expressed similarly extreme views in his private correspondence and other private writings.) Part of this might perhaps be explained as Schenker's awkward overcompensation for what would've been his remarkably humble origins back then (he came from a small village in what was then Austrian Galicia, now in modern Ukraine). Regardless, I think we nowadays have so many sources proving the relevance of melodic reduction/elaboration approaches (some of them quite early indeed, from the 16th-17th centuries) that to tie these analytical approaches polemically to Schenker and his specificities is really quite pointless, perhaps even misleading.

Ah yes, the good old "fascist dog whistle" argument. Schenker himself was an outright fascist. However, many theorists from the late 20th century who have come up with methods for analyzing tonal music have done so mostly on the back of Schenker's work. I'm also not suggesting you should read Schenker himself - his own work on what we call "Schenkerian analysis" is quite primitive and limited.

I'm curious what you would suggest to perform a modern analysis of Bach (what the original comment chain on this was about) if not Schenkerian analysis. I didn't see any alternative analysis tools proposed in your post, even though it sounds like you are educated on the subject.