It can be seen that the basic idea is simple.
Before the rise of modern science it was philosophers who investigated “the fundamental structure and nature of physical reality” (as it's often put). However, after the rise of modern science, philosophers shouldn't be still doing this without the help of science.... at least not in 2015!
As a consequence of that, The Every Thing Must Go position is against any “a priori metaphysics” or the search for “a priori truths”.
Prima facie, it's hard to make sense of this because I can't really believe that there's a 21st-century (or 20th century) metaphysician who would claim to be engaged in an entirely a priori pursuit. (Though perhaps I'm wrong.) In fact I'm not even sure what the words “a priori metaphysics” mean or if it would be achievable (in principle).
Anyway, if such a thing does exist, then James Ladyman and Don Ross class it as “neo-Scholasticism”.
Sometimes Ladyman and Ross's main criticisms of analytic metaphysics seem rhetorical – at least as they stand. For example:
i) That metaphysics "contributes nothing to human knowledge”.
ii) That metaphysicians are "wasting their talents”.
iii) That metaphysics “fails to qualify as part of the enlightened pursuit of objective truth, and should be discontinued”.
Sure, these positions can be argued for. However, it must now be said that some commentators say that they aren't argued for by Ladyman and Ross: they're simply stated.
What may happen here, then, is that those who follow the every-thing-must-go position will simply end up talking a different language to those who practice analytic metaphysics (or just plain metaphysics). And then it will come as no surprise that there's no mutual ground between them (or even a conversation). It will become like the situation between much Continental philosophy and analytic philosophy (at least until, say, the 1980/90s).
What Ladyman & Ross Do
The central metaphysical position of the everything-must-go school (if there is such a thing) is one of “ontic structuralism realism”. The fundamental aspect of this is the importance it gives to the mathematical relations or structures which capture the nature of physical reality (i.e., in physics). Clearly, then, if one wants to explore this position, then that's where to begin.
ETMG philosophers also class themselves as “neo-positivists”. They acknowledge that there were big problems with the original logical positivist school (if it ever was a school). That's not a problem because the logical positivists themselves realised that there was a problem with (much of) logical positivism. In fact it was mainly - or only - former logical positivists who destroyed logical positivism. (I doubt that other philosophers would have had the knowledge or skill to carry out that feat.)
It also seems that Ladyman and Ross are saying that metaphysicians should be scientifically-literate holists who should try to show us “how everything fits together in a broad sense” (as Nelson Goodman or Wilfred Sellars once put it).
In other words, the “ontological structure” of the universe is the domain of physics and science generally. Metaphysics, on the other hand, should attempt to find a unified and “cross-disciplinary” philosophical synthesis and analysis of how the sciences tell us the universe is structured. (Put that way, it's similar to Quine's position; though he didn't really emphasise cross-disciplinary unification as such.)
When a metaphysician says that analytic metaphysics is concerned with problems which aren't (strictly speaking) scientific (as well as when he says that it uses analytical and logical methods that aren't those of of science), then, I suppose, Ladyman and Ross may give the obvious reply:
The problems and tools of metaphysics shouldn't be distinct from science – even if they aren't identical.
Though if you were to take this position too far, metaphysics will simply become physics/science; or, at the least, a part of science/physics.
The problem is that no only may Ladyman and Ross throw out metaphysics and even all philosophy (if you follow their logic), it may even be the case that much science will also be thrown out too. (This point was famously made against certain positions advanced by the logical positivists.)
For example, what about empirically-untestable string theory? Is that “neo-Scholasticism”? What about some of the well-known mathematical and logical problems? That is, the ones which can be seen as “intellectual puzzles” and nothing more?
Everything must go?