Which of the Basic Assumptions of Modern Physics are Wrong?

The real problem is testing 'theories merging'

There are several areas where relativity and quantum mechanics merged, for example, in the discovery and theory of antimatter

But most of the experiments of relativity were on 'big things' like planets, and quantum mechanics on 'small things'

And between them, the real mystery: gravity. General relativity knows a lot about what gravity does but not so much about where it comes from

Edit: fixed GR for SR

I'm convinced that even if someone did prove that a basic assumption of modern physics is wrong, it would automatically be assumed in turn that the author is a crackpot, hence the work can be ignored. I'm convinced that the physics community isn't interested in the slightest in new ideas. Of course I'm automatically a crackpot (even beyond a conspiracy theorist) for even suggesting that.

As an example to how bad things have become in the realm of physics, it's safe to say that the vast majority of thinking adults believe that black holes exist, because so much major media has told them so. But when you look deeper you find that there's no definitive evidence. Sites like the Chandra X-Ray Observatory admit that, deep in their FAQ, but in words that many people can misconstrue as a technicality. When I point out in physics discussions that that there's no definitive evidence of black holes, I'm automatically labeled a crackpot, especially by the working physicists. One of my books suggests that this is a grant problem, as in black holes bring in a lot of grant money, so physicists must be careful to pretend that black holes are a definite reality in nature.

I think the problem here is that you're conflating the absence of evidence with the evidence of absence. There's definitely no definitive evidence for the existence of black holes, but (as far as I know) we have no evidence that contradicts current models.

Science works by coming up with a nullifiable hypothesis, then seeing how it holds up as evidence is gathered. When you see contradictions, you adapt your model. I think you're missing the middle step, where you see contradictions.

s/Special relativity/General relativity

Special relativity ignores gravity altogether, whereas general relativity sneaks gravity into the relativistic framework by equating it with curvature.

Both theories are, to me, frustratingly intangible. Like you said, we don't really know where gravity comes from. Really, we don't even have any sort of good intuitions for how to describe what it is. Stuff resists being shoved around. Stuff also attracts other stuff to itself. Einstein tells us these are both symptoms of stuff being curvature. It's all a bit too abstract for my taste (that is, I hope a more tangible/intuitive model will eventually win out). Field equations are predictive but not really descriptive. Is there a mechanism in there somewhere?

I don't see that to be the case. Physicists have been giving their utmost to try to crack open the standard model and prove it wrong for decades. And the same is true elsewhere as well. We thought we had a pretty good grasp on the nature of the expansion of the Universe, but it turned out that the expansion is accelerating. That was a huge reformulation of cosmology. We thought we knew about planetary formation, but once we started finding exoplanets we discovered many of our assumptions were wrong.

As far as black holes, we have not 100% direct evidence of them, but we do have many independent and very strong lines of indirect evidence. For example, we can see stars in orbit around an incredibly massive object at the center of our galaxy (Sgr A*) that is not luminous. There are no models that make sense for anything that could be so massive and so dark. Black holes are the only theory which fits all the evidence we have, that's how science works.