The way it varies though - mapping out the "dark matter" - suggests interactions with common matter both ways. So it's not like "the underlying fabric varies" - it really behaves like matter, forming clouds, strands, that "hair" - it's not a generic field or a generalized property of space "resulting in galaxies".
MOND suggests some unknown as of yet function mu(a/a0). If that function was to fit the observational data, it would be incredibly complex; nothing as elegant and common as common [something]/r^2 or sqrt(v^2/c^2). It would be more like a function to describe shapes of clouds basing on air flow, temperature and humidity.
We don't know any other physical entity that would behave that way - move, flow, gather - than matter. And while still some predictions are defied and we can't say for sure it's matter, if we compare the effects to known behaviors of various physical entities - waves, fields, energies - this one has strong similarities to matter and very few to others.
For example, space expansion is uniform; about all of cosmos expands at the same, flat rate that slowly changes over time, but is independent of location. Its source is described as "dark energy" but you can have justified doubts if it's really energy because its interaction with reality seems really unidirectional: it affects space, but the space and its contents don't seem to affect it. In case of dark matter though, the similarities are striking.
And if you think about difficulties of detecting it - it doesn't interact with electromagnetism... What percentage of our observation methods are not based on electromagnetism? All known matter keeps its structure - solid, gas, structure of atoms - due to electromagnetic forces. Bindings between atoms are all about electrons and protons interacting electromagnetically. All of light is EM wave. Most of non-electromagnetic observations like neutrina or collisions of neutrons - boil down to interactions that *eventually* produce some EM influence; be it an emitted photon, a neutron decaying into a proton and an electron, and so on - we observe them indirectly. If Dark Matter doesn't interact electromagnetically, it could sit right in front of our noses and we'd be unable to spot it. A solid chunk of dark matter could directly phase through a solid chunk of steel, because there's a lot of room between electrons and the nuclei and no force (electromagnetic!) that would prevent particles of the dark matter occupying locations in between; it could even phase through the nuclei because who says it needs to follow Pauli's Exclusion Principle? It's enough that it interacts gravitationally, and so your chunk of steel would exhibit 30% higher gravitational pull - but since its original gravitational pull is piconewtons, the change would be undetectable.