If I have a coherent laser beam and I shine it through some glass, the light will slow down because it will interact weakly with the atoms in the glass. However, the beam that comes out the other side of the glass will still be coherent. Why is this true? Because glass is not a solid, the atoms will be moving quite freely so when the photons interact with these atoms, I would expect the photons to be scattered in many directions. What is actually going on?
The light is interacting mainly with the electrons in the valence band (or the conduction band in metals). The oscillating electric field of the light causes the electrons to oscillate, and the oscillating electrons reradiate light that interferes with the incoming light and causes the change in the propagation speed that we describe with the refractive index.
This is a coherent process because on the scale of the wavelength of light the individual electrons are indistinguishable. The light sees the electron density as continuous and smooth so it is not scattered. You specifically ask (in the comments to your question) about amorphous glass, but it makes little different whether the material is a crystalline solid like quartz or an amorphous solid like regular window glass. The band structures of quartz and amorphous silicon dioxide are very similar.
Even liquids have a band structure, though this tends to be rather less well defined than in solids, so the argument above applies to liquids as well. This is why liquids like water refract light in a coherent way.
Having said all this, materials like glass are only approximately continuous and even though the wavelength of the light is about a thousand times greater than atomic scales there is some Rayleigh scattering. This tend to be strongest in liquids, and indeed Rayleigh scattering in water is easily measurable. It is less strong in amorphous solids and less strong again in crustalline solids. However even in liquids the Rayleigh scattering is small compared to regular refraction.
Have a look here and the links given to understand that classical light, and photons are two distinct concepts, but classical light emerges from the superposition of zillions of photons.
As a classical beam crosses a transparent medium, the photons are affected by the total lattice , i.e. the ordering of atoms and molecules in the glass. The 'slowing down" just means that they travel a longer path length, they only scatter elastically if there is no change in frequency. Coherence at the photon level means that in a transparent medium the phases between the individual photon wave functions are retained. This is what makes the medium transparent, by construction, otherwise it would be opaque. It means that the lattice distances are such that phases are not destroyed. The laser beam , being a superposition of these photons retains the phases too.
This would work for transparent fluids like water: At a $Δt$ the forces are such that an instantaneous lattice can be modelled, it just has a time dependence which is negligible for the velocity of light. ( Glass is not really a fluid)
In addition, if the photons cannot interact with a medium at specific frequencies, then the medium will be transparent, which is the explanation given here for the transparency of some glasses.