The common objections against Aether is the absence of reference frame. If the Aether is so dense, why we aren't detecting it's reference frame?

But this is just another misunderstanding of the inertial environment concept. In such environment the energy spreads in waves. The environment for waves spreading cannot be detected just by using of these waves - so it cannot exhibit reference frame for these waves. The inertial environment serving as a space-time for wave spreading is undetectable for these waves by definition.

If it's true and the vacuum is formed by inertial matter - why the observation of waves spreading through matter differs so significantly from spreading of light through vacuum? For example we know, the light speed is invariant to with respect to source or observer motion speed.

But this is the result of misunderstanding again. The observation of wave spreading in matter by using of light isn't equivalent the observation of light in vacuum by using of light, because of different experimental arrangement. We have simply a two energy waves involved in first observation, while the later one includes only light wave.

Therefore the observation of water waves by using of light cannot serve as an evidence against inertial model of light wave spreading in vacuum, as being observed by using of light.