The photon field is the vector carrier field that bears the electromagnetic force, so electrical charge must and will always interact with any photons it may be coupled to. Likewise for anything with a magnetic moment, for example, a neutron.
So all everyday matter must alter the electromagnetic field and thus can be thought of as having a refractive index, although a refractive index is not really a helpful way of describing this interaction when the wavelength is comparable to the widths of the atoms and molecules that make a substance up. Refractive index as it is wontedly thought of is only meaningful when the photons concerned are coupled to many atoms and molecules in the substance they are interacting with at a time. So if the wavelength is optical, a lone photon is coupled to all the atoms in a region at least of the order of a micron wide, therefore replacing the material by a continuum is a good approximation. But hard X-ray or $\gamma$ photons are coupled to very few matter particles at a time and the material is not a continuum with a refractive index but rather a lattice whose links interact one at a time with the photon concerned.
Some matter absorbs light. It can be thought of as having a refractive index with a big imaginary part. Physically, what is going on is most often that photons are being absorbed by electrons coupled to many other quantum oscillators within the matter. So the photon is less likely to be re-emitted but rather the energy is taken up into the matter as phonons, molecular vibrational energy and the like. The photon is thus lost from the light field.
A tree interacting with a radio wave is an interesting case. Here the wavelength is huge, and, from the farfield, the interaction can be modelled accurately by assuming that every atom in the tree is at the same point. You won't have to account for inhomogeneities and other complex variation of refractive index within the tree, it can be modelled as a point, isotropic scatterer with an amplitude to couple with the field modes; the coupling co-efficient with simply be the sum of all the coupling co-efficients of the atoms involved. Locally, however, things are quite different. The tree's complex spatial matter distribution, which can in principle be accurately represented by a variation of complex refractive index with position, will imprint a detailed "shape" into the scattered field. But, since the length scales over which the tree's matter varies are much, much smaller than the wavelength, these detailed spatial field variations beget evanescent waves, which cannot propagate far from the tree itself. So their effect is confined to the near field. From afar, the tree looks like an dielectric "speck".
The detailed science of calculating refractive indices is not really wonted to me, but it can be done for simple substances by enumerating all the vibrational and other energy states in the matter and working out the scattering matrix elements for the incoming / outgoing photons from these. Some raised states will not re-emit photons, and thus contribute to the refractive index's imaginary part. Others scatter photons elastically, thus contributing to the real part. For most substances, however, one needs to resort to tables such as those at the http://refractiveindex.info site or from glass manufacturer's data, specified as co-efficients for the Sellmeier Formulas, for example: it is too complex to calculate refractive indices for most materials. Refractive index does not only depend on composition, it also depends on the heating and annealing cycle a glass undergoes in its making. When you buy a block of, say Schott N-LASF31A glass, you are not only getting something made to a composition formula, it has to have undergone a detailed heatup cooldown annealing cycle to achieve the refractive index specifications the manufacturer claims.