Do the energy levels of electron orbitals change relativistically? When an electron emits a photon from changing energy levels, the frequency of the photon depends on the difference between the energy levels.
But if someone is moving with respect to the atom, the frequency will be apparently red shifted or blue shifted.
Does this mean that the energy levels of the orbits of the atom look to have different values if you are moving with respect to them? But, the apparent energy difference can be different depending on whether the photon is emitted towards you or away from you.
What's going on? Aren't energy levels of orbits supposed to be a fixed value given the kind of atom?
 A: To answer briefly, I'm not very confident in this answer and invite editing or downvoting as appropriate!.  
The energy levels of the electrons are determined via calculations of the electric potential/field around the nucleus.  The electric field is a vector field that transforms under special relativity and hence we account for any relativistic effects through moderation of this field.
A: The answer is yes, the energy levels transform according to the Lorentz transformations and are blue/red-shifted if the source is moving towards/away from the observer.
Replying to your last question, there is no reason for the energy levels to be the same in every frame of reference. This phenomenon is well known, two examples being:


*

*The emission spectra from stars, which are red-shifted as galaxies are moving away from each other. Actually the red-shift allows cosmologists to gain a lot of knowledge about the Universe.

*Some applications of the Mössbauer effect, in which the shift in frequencies is actually exploited, by tuning the relative speed of the source and of the absorber, to modify the emission frequency making sure it matches the absorption frequency. See for instance: http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/mossfe.html
