The difference between aether and dark matter is that with aether theories, experiment after experiment showed repeatedly that it didn't exist, or at least didn't work the way it was supposed to. There was Fizeau's experiment in 1851 which largely ruled out any aether drag effects, the Michelson—Morley experiment in 1887 which established the constancy of the speed of light and ruled out the aether wind hypothesis, the Trouton–Noble experiment in 1903, the Rayleigh and Brace experiments between 1902 and 1904, ... there was a wealth of experimental evidence available showing the problems with aether models. Also it wasn't "nearly consensus" that aether existed, there was quite a lot of debate all throughout that period as to whether light was a wave (one that travelled in a presumed medium — an aether of some sort) or whether light was a particle or "corpuscule" (and hence a form of matter that did not require a medium within which to propagate). Various people proposed either/both wave- or particle-based theories of light and experiments continued to both confirm and refute aspects of each proposed model, all the way from their inception into the early 20th century. The problems with both kinds of models only really began to start being resolved with the advent of early quantum mechanics and the emergence of wave-particle duality as a feature in physics.

With the dark matter situation however, you have dozens of kinds of observations that are all in general agreement about dark matter, while those same observations are largely contradicted by the predictions of modified-gravity models. Unlike with the aether, this isn't a situation where nobody's model fits all the data; with dark matter there is a clear matter-based model that does fit all of the data, and then a bunch of alternative models that don't. That's a pretty huge difference.

>I’m far from an expert, and dark matter seems from what you write proven by many independent sources. But, I can guess, for many, it smells like an esoteric substance stubbornly refusing to be directly identified.

And this is the crux of the public relations issue on this topic: really only the people who are "far from experts" who aren't actually familiar with all of the evidence feel that way. Among actual experts, the consensus is that dark matter exists and that modified gravity models don't actually work. The only people who really have a problem with dark matter anymore are the ones who are uninformed about it. :(