Anything about non-440 pitch standards being the "frequency of the universe" or "healing" is arbitrary nonsense. As you know, A=440 is the standard concert pitch in most of the World for ages now. Due to something called pitch inflation, some orchestras deviate to as high as A=450, though generally it's more along the lines of A=442 or so, to sound comparitavely punchier and more lively than other neighboring areas orchestras.
The A=432 movement is some pseudoscientific nonsense with loads of baked-in antisemitism, scientific-illiteracy, and Eastern-Tokenism. The actual history of A=432 is that Italian composer Giuseppe Verdi's preference was for a tuning standard slightly less than the French A=435 standard of the time, though there wasn't really a concrete way of determining exact measurements of hertz, so all tuning forks from the time were completely arbitrary– it was just about matching pitch and having a locally standardized tone of reference, rather than anything scientifically based. Verdi's tuning fork measures as roughly A=432, but to be clear, tuning standards of the time were almost entirely arbitrary. The only thing that does matter and that ever did really matter is the ratios between the notes; that is to say, the temperament system used, whether that's just intonation, 12-tone equal temperament, some other TET/EDO system, a meantime system, or something else.
The only time where non-440 tuning standards come into practice for legitimate cause is:
- Historical music: While there was no true set pitch standard for the Baroque era, the median pitch of tuning forks of the period is roughly 415hz, so A=415 is commonly used for historically accurate performance of baroque pieces. 415hz is extremely close to an Ab in A=440 however, so the main takeaway is that Baroque compositions should be transposed to be played a semitone lower than written, and this is what's commonly done in most historical performances that aren't going to the lengths of accuracy to also acquire instruments of period correct construction and wear period correct attire.
- Pitch matching, which itself falls into a few sub-categories:
- Fixed-pitch instrumentation or samples: Let's say you are playing in an ensemble with an organ. You can't retune the organ, and it may not be perfectly analogous to an A=440 pitch standard, either due to pitch degradation with age, lack of standardization when it was created, electrical differences causing a tone wheel organ to play slightly higher or lower due to motor speed, etc. In that case, all other instruments would tune with the fixed-pitch/non-tunable instrument as their reference pitch. This is how most bands have tuned for decades when there's a piano, electric piano, analog synthesizer, or organ involved. This is also no different from when you tune your guitar to be in tune with itself relative to one arbitrary string, without knowing if you're tuned to A=440 or not- that's why so many live recording of bands in the 60s and 70s will incredibly inconsistent, with some recordings being around a quarter step sharp, or others being 1/4 or 3/4 steps flat. Believe it or not, Led Zeppelin, AC/DC, and Van Halen weren't trying to tune to A=432
– they were just tuning to each other.
- Resonance: You might tune to the resonance of a room to induce feedback more easily, or you might tune to avoid the resonance of a room to stave off unwanted feedback. An instrument might have a wolf tone at a certain pitch standard, but once you tune a few cents up or down, it's no longer inline with any of the chromatic pitches you'll be using. It's all fair game, and it's pretty common.
- Poorly-synchronized Analog recordings: You've surely heard records where everything is, say, 10c sharp/flat on a record, so it sounds crappy when you try to play along. It's not likely that the band recorded at A=432 to be spiritual or A=420 or A=469 for the memes; its most likely that somewhere in the production chain, one of the tape machines was running at slightly the wrong speed. It could be in the recording stage, or when the tapes were bounced to a new machine for the mix down, or the mastering stage, or even when cutting the lacquer stampers for a vinyl release. You have a lot of stages in the recording process where you're relying on crude motorized machines to spin at an exact speed, and it's easy to have electrical or mechanical inconsistencies turn, say, 30in/s into 29.9 in/s. Who's to say that your turntable is running at 33 1/3 rpm, and not 32 7/8 rpm? Lot's of ways you can accidentally drift from the recorded pitch, and it takes more than just a few cents of deviation for it to noticeably mess of the formants of vocals. That's why a lot of turntables have speed adjustment. Digital stuff is all based on bitrates and crystal oscillators with much more precision, so it's not a big issue, but in the analog domain, anything goes!