First we may clarify what is exactly meant by "following Maxwell". For example in electrodynamics (weak interaction switched off) there is interaction between electron field and photons. Is this Maxwell? Classical Maxwell equations include the interaction of electromagnetic field and current and charge densities, but they don't include equation of motion for the charges. Nevertheless, we can say that in quantum electrodynamics

1. photon obeys Maxwell, because the electrodynamics Lagrangian is identical to the classical Lagrangian which produces Maxwell equations (plus equations of motion for the charges)
2. photon doesn't obey Maxwell, because due to quantum corrections there is an extremely weak photon self-interaction, which is absent in classical Maxwell.

See that the problem has nothing to do with masses (photons remain massless in QED), Glashow-Weinberg-Salam construction of electroweak gauge theory or Higgs boson. The apparent Maxwell violation (here, scattering of colliding light beams) arise because on quantum level one can't prevent the electron part of the Lagrangian from influencing the outcome even if there are no electrons in the initial and final state. Whether or not is this viewed as Maxwell violation is rather choice of words. The electromagnetic field still obeys equations which are free Maxwell + interaction with non-photon fields, but there are effects which we don't see in the classical case. Also, those violations of Maxwell are perfectly compatible with Lorentz covariance.

In the case of vector boson mass generation, one may again formulate it in two different ways:

1. the vector boson follows Maxwell, since it obeys equations which are free Maxwell + interaction with Higgs
2. it doesn't follow Maxwell, because the interaction with Higgs manifests itself as effective mass

Again this is mere choice of words.

Now you mentioned the linear combinations of non-physical gauge fields which give rise to physical photon and weak interaction bosons. The way you put it it seems that the underlying fields, which correspond to U(1) and SU(2) gauge group generators, are massless and the mass arises somehow in the process of combining them together. This is not the case. The underlying fields all interact with Higgs and therefore are all massive. Even if the current neutrino affair lead to slight revision of photon masslessness, the underlying fields would be "effectively massive" by interaction with Higgs (I put "effectively massive" in quotes because it's pretty weird to speak about effective properties of fields which are not measurable).

Of course, your overall point is true - there is no fundamental reason why photon couldn't obtain a tiny mass by the Higgs mechanism. Photon masslessness isn't a theoretical prediction of the SM.