You're a wonderfully gifted lot. A while ago I found, elsewhere on the Forum, comments indicating the effect of experience (called "practice" when done formally) in different contexts on how one learns. Many of the postngs here have again reinforced this theme, although it hadn't penetrated my thinking on this,
For reasons I've mentioned elsewhere, I avoided learning to read music but singing and playing with many experienced people over the years has taught me a swag of theory and you've pointed out the various other entry points people use.
The recent comments about Cat, Dog Etc remind me of an occasion Mike Jackson (harmonicas) Tony Suttor (button accordion) and I (Anglo) were playing; Hyde Park during the Festival of Sydney. We'd started on of our band brackets (three 32 bar 'polkas', each played twice through) and, by the end of the first time through the third tune, Tony and I could see that Mike had a full head of steam up and would probably not be able to stop; the pace was pretty brisk. At the beginning of the last 8-bar phrase Mike yelled out "D!" By some miracle we all, in unison, went into "Soldiers' Joy."
More germane to the thread, when I was learning to play the Anglo I had only a 20 button Lachenal in C & G, when lots of tunes in sessions were in almost anything but C. My ear was OK picking up melody well enough but I couldn't discern. by ear, which key the tune was in. I relied on Tony's playing of his ADG accordion; if his fingers were on the inside row (G), I could reasonably attempt it on my G row. At one session I had to lean past a very good fiddler to see Tony's fingers; they were on the inside row.
"Ah, G" I muttered. "A minor" she corrected me. At that time I knew just enough theory to be dangerous and knew that Imogen Holst's book had described minor scales as requiring more notes than you could get on a single row melodeon (which could play many minor scale tunes well enough) or even a 20 button Anglo. This confused me until I met a fiddler/violinist with seriously classical training but folk tendencies who explained the relationships between modes, scales and keys.
There are others on this thread who've posted very learnedly about this elsewhere and I have no wish to divert from the topic but the postings above have reminded me of the different gaps we have, the various ways people learn and the breadth of skills on offer.