Physics also has an unfruitful history of invisible stuff: ether, strings (string theory), etc.
Personally I'm glad something other than dark matter is being considered. I was only told that the rotational velocities of galaxies did not match the predictions. IME simple explanations tend to work better for mechanics in physics (until quantum mechanics...)
Right, and there is also evidence for dark matter.
In this case we have a theoretical mode, but we later notice our empirical data doesn't match this. Both MOND and dark matter are an attempt to patch up our existing theory to explain what we have seen. This is less compelling, because it is post-hoc and these theories might just work because we force it to work by over fitting. To use an analogy to machine learning, it is like training on your test set; no on is impressed when you then have good performance on your test set.
With that said, I think that point of view would apply to both theories equally.
There have been several independent observations that are explained by dark matter, and it's not like the theory for dark matter was specifically changed to accommodate those observations. The most well-known is around gravitational lensing, as the amount of observable mass in clusters of galaxies does not match the amount of distortion that we observe. There are however several others. This kind of independent validation of a theory from other angles is a textbook case of how theories are validated - they are proposed to explain one thing, but turn out to also explain other things.
MOND meanwhile has a much tougher time explaining the other observational evidence. It has had to be extensively patched to fit the other cases. Additionally, as noted elsewhere in the comments, neutrinos are not dissimilar to dark matter. Both are forms of matter that it do not interact electromagnetically, making them all but impossible to detect directly. Theorizing that there is more than one such type of particle is not very much of a stretch. Taking that into account, MOND seems to be a much more complex solution than just having another type of matter with properties similar to those we have already seen.
Almost all of the skepticism around dark matter comes from outside of the scientific community, and I think both the name and it being lumped in with dark energy (which is just a placeholder, not an actual validated theory) are part of what contributes to this. While obviously the consequences of this skepticism are significantly less dire, the reasons for it seem pretty similar to those of climate change skeptics - primarily tied to human intuition.
General relativity might be wrong, but it's probably not over-fitted because it's quite simple as far as theoretical constructs go.
And it has a pretty good track record. Both black holes and gravity waves were "invented" because the theory seemed to indicate that they should exist, even though there was no evidence yet. Both were spectacularly confirmed last year.
That said, we know there is some shortcoming in either GR or quantum mechanics (or both), because they don't agree under certain conditions. Dark matter, being a gravitational phenomena that seems like it might be a new kind of particle, is potentially in that same area.
In my opinion Verlinde's theory is a better candidate as a replacement of dark matter, since it doesn't require changing the theory of gravity as drastically as MOND does. That said, his theory does require a combination of general relativity with quantum physics, which is tricky. Compared to both just adding a bit of dark (not necessarily invisible) matter is a lot simpler.
Inventing and then testing, though. As you said, GR got a huge boost last year, still being tested a century after being proposed. That's how science should be!
We know the darkX behaviour and we have some ideas as to explanation, but far from being proved in the way GR has been.
Dark energy, dark matter, string theory. Lots of IQ being poured into them, with a reasonable chance they're not the answer.
And like dark matter, black holes point out shortcomings in our theories--they are ground zero for the incompatibility between general relativity and quantum mechanics.
And yet, even though we don't fully understand them, there is not much public doubt that black holes really exist. To the contrary: they are quite popular!
I'm not arguing that just because we think black holes exist, therefore dark matter must also exist. That's bad logic. I'm just pointing out that a lot of the popular concerns with dark matter are not unique to dark matter.
Scientific theories are generally not just amalgamations of tweaks. General relativity is internally consistent, explains so much, and just got a huge boost last year with the first detection of gravity waves... which BTW are invisible stuff that was invented based on theory. It is not lightly cast aside.