...the leading tone wants to rise to the root...
Basic theory says things like...
- the leading tone is a half step below the tonic
- in a proper cadence the leading tone moves to the tonic, or if in a inner voice it may move down to the dominant.
...of course that isn't a complete theoretical overview of the leading tone.
A claim that theory simply says 'the leading tone moves to the tonic' is incomplete, and as a description of actual musical art it complete nonsense.
I think a lot of misunderstanding of music theory come from taking incomplete theory ideas and then misstating them as laws.
...saying that certain intervals elicit certain emotions is taboo?
Again, the specifics of wording matter, and it's easy to misstate things. 'Certain emotions' is not the same meaning as 'emotions.' Obviously intervals and all other musical devices can elicit emotions. The problem is trying to make certain claims like minor thirds are sad or diminished fifths are scary. Statements like that are too broad and won't withstand any scrutiny.
Good theory texts will describe expressive possibilities - not one to one formulas - and provide real musical excerpts to illustrate the ideas.
I think you want to distinguish between what music IS - an art - and music theory which is a way to describe music with some objectivity.
Art does whatever it wants. The theoreticians try to make a theory to describe what the art did.
Keep in mind it's a theory about art not a scientific theory. Acoustics is science and not the same as music theory. Confusing the two is another common mistake.
Music Theory: Facts or Hierarchy of Opinions?
Neither. I would say it's more like qualified statements about common musical practices using established terminology.
Just adding something about rules after reading @topo-morto's answer.
You often hear "there are not rules in music." Well... there are, and there aren't. We need to distinguish music theory from specific style practices and pedagogy.
No parallel fifths is a good example to use.
These is such a rule... in Fux's species counterpoint. That's pedagogy.
You will see parallel fifth scrupulously avoided in most "classical" music... except in musettes, fanfares, and other specific cases. It's called common practice. On the other hand, in heavy metal parallel fifths are practically a requirement! That style.
Two voices moving in parallel fifth differ only in one voice being an exact transposition of the other. There is no difference in melodic contour between the two voice. Pitch-wise the two voice exhibit very little independence. That's an objective description, non-specific about style, is neither prescription nor proscription, and makes no aesthetic evaluation. That's music theory.
And just as an aside, I think the only thing acoustics and math will tell us about parallel fifths is that if you use an instrument with fixed tuning, it is mathematically impossible to play two absolutely perfect, consecutive fifths.