The original post wasn't talking about having an opinion on someone else's theory. It was making up a new theory. If two experts argue about something, and they explain it well to you, and you form an opinion on this, you will probably be right. There's still a pretty good chance you'll be wrong, so you shouldn't form a strong opinion, but you can get higher than 50%. If you make up your own theory, then you are distinguishing one out of a huge number of possibilities without anyone explaining anything to you. Your theory will probably be nonsense. If it isn't, it will probably be fundamentally flawed. If it isn't, it will probably be something that can be readily disproven. If it isn't, it will almost certainly not be the simplest explanation. You can easily make an accurate opinion in this situation, by assuming that your theory is wrong.
My central point is that the two things you described are empirically identical
They are identical to within measurable error. However, there is a difference. There are ways to detect entangled systems. It just gets exponentially harder as you increase the size of the configuration space by adding particles or letting them move more etc. In principle, no matter how much has to get entangled for a waveform to collapse, you could entangle more than that and check to see if it stays entangled.
and the only difference between them is which parts of the math are defined as "existing".
No it is not. The math shows how an entangled system of particles evolves. The Copenhagen interpretation does not say that after a certain number of particles get involved it stops being "real". It says that it collapses, in a manner that presumable could be precisely defined, but since there's neither theory nor empirical data behind the idea, they can't actually tell you what the definition would be.
From what I've heard of the two arguments so far, I don't actually see why you need a background in physics, or any empirical knowledge at all, to answer this question once it has been posed.
Of course you don't. You're not a domain expert. It's hard to see why you need the background knowledge, when you don't have the background knowledge and you can't see how it helps.
There are times where the background knowledge doesn't help much. Like understanding the Born probabilities, for example. If the domain experts consistently tell you that being a domain expert isn't going to help, then you can accept that being a domain expert probably isn't going to help. Even in these situations, you shouldn't form strong opinions. It's not so much that an amateur understands it as well as an expert as it is that an expert understands it as badly as an amateur. You're just as likely to be wrong as normal. It's just that the experts aren't any better off.
There are a great many ideas which don't have enough carefully-measured evidence to be sufficiently confirmed as scientific fact and accepted as such by the scientific community (a recent joke was "While the Higgs Boson has not been discovered yet, its mass is 125 GeV"), but don't have enough carefully-measured evidence to be ruled out yet, either. Do any of the tools of the LW community help narrow down which ones are more worthy of consideration than others?
Eg:
* Cryonics as an arguably reasonable bet for its cost: proto-science
* Cryonics as a surefire way to achieve immortality: nigh-certainly pseudoscience (unless it's the method by which your Everett Immortality keeps you alive)
* Using math to demonstrate that taking classical physics and adding determinism results in MWI-style quantum physics: proto-science.
* Using math to demonstrate that quantum physics proves Christianity is true, from a certain point of view: pseudo-science
* Tubulin might self-organize into microtubules capable of computation on a sub-neuron scale: Possibly proto-science
* Tubulin architecture is 'quantum' in nature and that is what gives rise to consciousness: Probably pseudo-science
* 'Quantum consciousness' means anything is possible: Downright silly
* The E8 Lie group can provide a system for organizing the properties of subatomic particles: Proto-science, perhaps
* Heim theory is useful for predicting particle masses: Pseudo-science, probabilistically
* Using the Bullet Cluster to claim that dark matter is a better theory than Modified Newtonian Dynamics: proto-science
* Claiming that dark matter is made of 'anapoles': Proto-science, perchance
* Suggesting that dark matter is actually gravitational leakage from MWI 'parallel universes': You tell me. (But if it's true, then since I can't seem to find any previous serious discussion of this idea, I get to name part of it after myself, right? :) )
These may not be the best examples, but they're the closest ones I can think of to the boundary. If you know of any better ones, feel free to comment with them.