That's not what I claimed. We have a very good curve to fit our sample data; this doesn't mean that "anything goes" because we don't know everything, it only means that we should be careful not to assume that we know everything because our curve fits so well to the data we do have.
Part of that is confirming that things we expect not to work do not work. We shouldn't fear or avoid testing things simply because they disagree with our understanding, because testing them may confirm our understanding.
I think I get what you were going for, but I think David Deutsch's idea[1] of "explanations that are hard to vary" may be a better metaphor. The basic idea is that we can come up with all sorts of ad-hoc explanations for any particular phenomenon, but if you can just arbitrarily change your explanation (the means) in response to events (data) then it's manifestly not very good at prediction (the goal).
Just to get back on track: The point is that we have a huge number of explanations, currently, which are "hard to vary". You need a commensurate amount of "hard to vary" explanations to counter that. That's why it's very hard to overturn e.g. the 2nd Law of Thermoses, erm, Theormodynamics.
[1] I think, from "The Beginning of Infinity"... Actually, I can't remember if he cited anybody else for this idea, but I can say that it's the first place I came across it.
I encourage anyone to read it, even laypeople. It's a great read if you want to think about science itself as opposed to just thinking about the "latest development in $SCIENCE". (Where $SCIENCE could be Physics, Biology, Medicine, ...)
There are a few bits in there that may be hard for the layperson to understand, but I think the overall point is amazingly well made.
I don't agree at all: being so quick to dismiss energy-momentum conservation is pretty much the same as anything goes. Noether's theorem runs really deep. For an example of an existing (non-crankpot) effort, have a look at the attempts to find Lorentz violations: https://en.wikipedia.org/wiki/Modern_searches_for_Lorentz_vi... That's more like what it looks like when people try to do it seriously.
I don't think this will result in dismissing of conservation of momentum.
But because many thought it did, it's been an incredible uphill battle to get this thing tested; yet throughout tests it shows strange outcomes. Something odd is going on, and perhaps the simple outcome is that we find a better way to perform the tests.
To me, that's a fantastic outcome and I'm dismayed it's taking such a _political_ fight to arrive at it.
And that will likely remain true. Thanks to testing this, we'll end up with better testing processes.
Why is it such an uphill battle to engage in actions that have positive outcomes like these, simply because they challenge our core understanding of the world? At the least, we end up better equipped to measure and test future experiments.
Part of that is confirming that things we expect not to work do not work. We shouldn't fear or avoid testing things simply because they disagree with our understanding, because testing them may confirm our understanding.