I don't have the scholarship to give you a survey of several schools -- perhaps someone else will.
The way I see it is that schools will have a "canon". I think that's a bit a analogous to the "curriculum" of a school -- and different schools have different curricula ... almost by definition -- and therefore (i.e. to that extent) your question and/or my answer to it might be just trivial, or unsatisfying.
Or it may "beg the question" i.e. whether there even are different schools of sects of Buddhism, e.g.,
- @Lanka Theravada Buddhists don't really recognize other schools. Mostly historians do that. So it's just Buddhism for us. – Sankha Kulathantille Aug 13 '15 at 13:33
- And we do recognize other schools, it's all Buddhism for us :) – Andrei Volkov♦ Aug 13 '15 at 15:56
Now just consider the Pali canon, for example -- I thinks that's "the canon" for many Buddhists.
Trivially if something is in the canon then it's canonical, and if it's not it's not.
If you ask, "what makes something canonical?", then you might get an answer like, Buddhist councils.
If you ask, "is that (is a, is any) canon necessary and sufficient?" --
Which sects or schools reject Nagarjuna's metaphysics? On what grounds do they do so?
I don't know that they even know or care?
I don't know if this is a good analogy, but ... "How can there be people who haven't thoroughly studied Einstein's theories of relativity? How do they even explain the gravitational lensing of light, without it?" -- someone asking these questions might think that Einstein's theories are utterly fundamental to understanding the nature of the universe we live in -- for other people ("normal people", if you'll excuse my putting it that way) that's completely missing the point, quite irrelevant, nothing to even think about.
How do they deal with the difficulty that Nagarjuna proves all theories of Reality except his own are logically indefensible?
Quite. Well I suppose that Buddhism isn't necessarily "metaphysics". I think I inferred from this comment of yours that you see Taoism too as metaphysics (or what you call a "(perennial) philosophy") -- I don't know, maybe it's something else: practical, a science ... a history, a narrative (see also e.g. "is medicine a 'science', or an 'art'?") ... whereas "metaphysics" are even less relevant, more of a niche interest, than "physics" (if you'll forgive my saying so, that's me having studied physics but not formal philosophy).
Practically, I think that the suttas' summary is something like, "all sankharas (n.b. nibbana is a dhamma not a sankhara) are dukkha" -- and "both (i.e. all dhammas, including nibbana and sankharas) are anatta").
In contrast, I think that (correct me if I'm wrong) N's summary is that "everything (including nibanna) is sunyata".
Maybe the suttas aren't trying to be "logically defensible" -- they're trying to be "helpful descriptions" ... for people who have "ears to hear", and "little dust in their eyes".
I wonder whether some Buddhists cherry-pick from these -- or do those who reject or accept one of them tend to reject or accept all three?
I get from the suttas that the Buddha (and, following his example, some Buddhists) might treat that or any other kind of question as false dichotomy -- e.g., "Q: Is it this or that, or both, or neither? A: none of the above, or no answer."
Questions like, I don't know, "Are things empty or not? Are two truths, or only one, or none?" are just -- might be (at the risk of sounding rude) be called -- examples of papanca.
I mean, after you have studied -- and if you study -- Nagarjuna, then you may understand what he's saying ... and why he's saying it i.e. why it's helpful or beneficial, useful, practical, worthwhile.
Maybe you should know, though, that lots of people simply haven't (studied N that well) and don't (understand what good about it and exactly what he's saying).
If you try to make comments (brief remarks or answers), which presume that people have read N and that they understand it in the same way that you do, then your comments may be misunderstood, or baffling -- see e.g. here,
Buddhist discussions online have a tendency to attract "there is no spoon"* answers
I guess another example might be the Zen story, titled Nothing exists ... an example of the doctrine being -- variously, I guess, depending on I interpret that story -- hard to fathom, shallowly repeated, easy to misunderstand, or missing the point entirely.