Are Neutron stars transparent? Neutrons have no charge so they would not, I think, interact with photons.  Would a neutron star be transparent?
 A: Neutron stars are not charged, but they definitely have magnetic dipole moments, and these DO interact with the electromagnetic field.  
A: Light with wavelength $\lambda\gg10\,\mathrm{km}$ can pass around a neutron star thanks to diffraction, even if the star is made of a perfectly absorbing material. That's exceptionally low-energy radio waves, though, and pretty different from what you probably had in mind.
A: You can think about it in more practical terms. It is known that one metre thick lead can stop very energetic $\gamma$-photons. Then, given that a neutron star is billions of times denser than lead and several kilometres across, it is not very likely that a neutron star will be transparent.
A: Neutron stars are one of the least transparent objects in the universe.  There are still lots of protons and free electrons, and most importantly the density of these charged species is extremely high.  Also, the quarks, which constitute neutrons, are charged---so due to their density, I would guess (hopefully an expert will chime in) that that is also plenty to keep them optically thick.  Definitely once you get to gamma-ray energies, neutrons will interact with photons.
