I appreciate your attempt at balance, but I still fundamentally disagree. Math is universal. The arithmetic and other math basics we learn in grade school is both (A) not very culturally-biased and (B) often not taught well.
There is so much cultural baggage and assumption in the notation-focused "music theory" that is not present in mathematics. When we talk about numbers of things in math, there's no doubt we're describing something objective about reality external to culture. There indeed exists two apples or four apples. The concept of "four notes" is rarely objectively valid because almost everything in music is subjective.
"Music theory" basics are much more analogous to the elementary-school versions of linguistic grammar. And most elementary teachers' understanding of grammar is actually full of claims that are wrong, even though there's something to the gist of it. When we go to "English" class, we expect to learn about English and don't think our lessons apply to all languages. We should similarly not teach one particular language of music and call the lessons "music" without qualification. We should further recognize that grade-school definitions of nouns and verbs do not all hold up under scrutiny.
When "music theory" of the sort here is taught well, it is about as valid and useful as grade-school pedantic, prescriptivist, grammar — the sort that treats minority dialects as "bad grammar". Insisting on music theory being this notation-jargon from classical Europe is like saying that African-American dialects have poor grammar, when actually there are careful and consistent implicit rules in those dialects that sometimes carry useful meaning that standard American English doesn't even have a way to achieve.
I actually don't think we completely disagree here.
First, I definitely didn't intend the parallels with math to extend any further than the problems of perception with regard to how they are taught versus how they are practiced by scholars. Music theory is an art-related discipline and very much culturally inflected.
And this makes sense. Most music theory (in the West at least?) does focus on Western classical music, in large part because Western music has a literate tradition (see Taruskin) that most other musical traditions lack, which allows us to treat the compositions themselves as texts/objects more easily than other musics.
Even within Western music, we tend to use style- (read culture-) specific analytical tools. It doesn't make sense to use harmonic analysis for Stravinsky, and it doesn't make sense to look for twelve-tone rows in Mozart. In general we use a combination of language that composers used and thought with (so for Mozart, think keys and counterpoint) and techniques that arose from observing the style after the fact (in this case, for instance, sonata form, or Schenkerian analysis).
All of these techniques are culturally biased because, as you've pointed out several times, music is psychological, and therefore rooted in culture. Meanwhile, it makes sense to analyze, for instance, Indian classical music using rhythmic modes.
So, coming around to your analogy with elementary school grammar education, I think you're right that there is a prescriptivist parallel here -- learning that parallel fifths are not allowed, or that the second theme in a sonata always modulates to the dominant, or even that there always is a second theme in sonata, all of these do not accurately describe all music, or even all Western music of the common practice period. They are artifacts of the particular techniques being used. The original description of the sonata came into being around the same time as prescriptivist grammar (and has had a great deal of improvement since then -- read Rosen if you haven't already). Species counterpoint and Bach-style chorale harmonizing came about to describe specific styles, and to be used as exercises for composition students in the 18th-19th Centuries. The fact that those two things in particular (which I think are the most grievous examples of what you're talking about) are still included in music theory education is possibly counterproductive, especially since they are treated as sets of rules, rather than as historical examples of the composition pedagogy that the Western classical composers themselves were subjected to. Teaching Fux as anything other than "this is how Mozart and Beethoven learned to write counterpoint" is silly.
So that's the prescriptivist parts. However, where we disagree is that I think there's still a lot here that's useful for descriptive purposes. It's difficult to talk about classical music within its cultural-intellectual context, which I think is necessary, without these tools. You can argue that any interval can be dissonant with the right timbre, but if those timbres are rarely used in the repertoire you're describing, it's not much use is it? The 18th and 19th Century composers thought about dissonance a certain way, and if you're analyzing their work as art objects (cultural objects) rather than physical objects, you have to at least take that into account.
The problem I have with trying to casually learn music theory is that I cannot separate what is "real" and what is "syntax". For example, I can trivially see that "beaming" is entirely syntactic, but the difference between 3/4 time and 6/8 time is far more confusing.
Music notation just seems really really suboptimal for actually understanding music (music software uses totally different notations/interfaces for a reason), and all music theory seems obsessed with it.
In fact, beaming makes the difference between 3/4 and 6/8 clear. But even if it didn't, you can't divorce the cultural object from it's notation. Once you're trained, traditional music notation is pretty optimal for reading music for performance, and you have to remember that that is the purpose of music notation. All alternative notation systems I've seen fail this simple test: once I've learned this, would I be able to play music I've never seen before reasonably well the first time? I've never seen anything that works as well as traditional music notation for that.
Meanwhile, music theorists are "obsessed" with notation only insofar as the music they study is written using that notation. You seem to have skipped my previous comments -- music theory, even at this basic level, has little to do with notation. You read it as notation obsessed only because you're not thoroughly enough steeped in the notation. Reading and writing music notation is as natural to a musician as writing in English is to you. It would be strange and counterproductive to insist on using nontraditional notation when every musician who plays the repertoire you're studying already reads the standard notation, and all the repertoire you're studying is written in it.
There is so much cultural baggage and assumption in the notation-focused "music theory" that is not present in mathematics. When we talk about numbers of things in math, there's no doubt we're describing something objective about reality external to culture. There indeed exists two apples or four apples. The concept of "four notes" is rarely objectively valid because almost everything in music is subjective.
"Music theory" basics are much more analogous to the elementary-school versions of linguistic grammar. And most elementary teachers' understanding of grammar is actually full of claims that are wrong, even though there's something to the gist of it. When we go to "English" class, we expect to learn about English and don't think our lessons apply to all languages. We should similarly not teach one particular language of music and call the lessons "music" without qualification. We should further recognize that grade-school definitions of nouns and verbs do not all hold up under scrutiny.
When "music theory" of the sort here is taught well, it is about as valid and useful as grade-school pedantic, prescriptivist, grammar — the sort that treats minority dialects as "bad grammar". Insisting on music theory being this notation-jargon from classical Europe is like saying that African-American dialects have poor grammar, when actually there are careful and consistent implicit rules in those dialects that sometimes carry useful meaning that standard American English doesn't even have a way to achieve.