The ether that Michelson and Morley proposed to detect (or, more precisely, find the Earth's velocity relative to) had to fulfil certain criteria. It had to be able to pass through normal matter more or less unhindered (otherwise radio waves couldn't go through walls). It had to have some kind of internal structure, since light waves were polarisable and, hence, transverse.
That's a fairly straightforward and simple model, as these things go.
But Michelson and Morley didn't detect any velocity with respect to the ether, ever. So it's a wrong model. People began to add bells and whistles to the theory, such as "ether entrainment". That's the idea that ether does in fact interact with normal matter. It is dragged along with normal matter - so the Earth drags ether around and we are always at rest with respect to the near-Earth ether (or close enough for Michelson and Morley to miss the difference). People began to try things like Michelson and Morley experiments with one arm shielded by a lead tube to provide more entrainment in one arm than the other.
But, along came Einstein with a complete, simple (at least as Occam's sense of the word) theory that explained Michelson and Morley's experiments - and Fizeau, etc. There is no need for complicated ether-drag models for which there is no experimental evidence. In fact, the GPS strongly suggests that there's no such thing (since the satellites are very precise clocks a long distance from the Earth, and they still act as if there were no ether).
Strictly, the Lorentz Ether was never ruled out. However, as I understand it, the Lorentz Ether has no physical properties - it just is. In other words it's a "presentist" interpretation of special relativity, as opposed to the "eternalist" picture (the block universe) that is (I think) the more popular view. It is not the ether that Michelson and Morley tried to find, however, and is most definitely not made of matter.