Would light emitted from a white hole be red-shifted or blue-shifted? if it's not that straight-forward, what factors would effect the resulting appearance of light emerging from a white hole?
 A: the emitted matter, includes light, will blue-shift because the white hole is unstable(Schwarzschild solution). actually, so called'blue-sheet' will be formed at partical horizon by 'cut-slide' model, the energy will be infinite at blue sheet. you can see this reference:Death of a white hole. For calculation, you can refer to my another answer why wormhole is unsatble
A: The definition of a static gravitational Doppler shift is in terms of emission by a stationary emitter and detection by a stationary detector. Stationary observers only exist outside the black hole and white hole horizons, so it actually doesn't make sense to talk about the static gravitational Doppler shift of light that is emitted from inside a white hole horizon or observed inside a black hole horizon.

Would light emitted from a white hole be red-shifted or blue-shifted?

So the answer to this question is that it depends on the state of motion of the emitter. The shift can be either red or blue, and in fact a given emitter's radiation will be observed as red-shifted by external observers at some angles, but blue-shifted by external observers at other angles. This is analogous to the fact that for an observer inside a black hole horizon, radiation coming from outside will be blue-shifted if received from some directions, but red-shifted if received from others.
related:
What Would a White Hole Look Like?
What will the universe look like for anyone falling into a black hole? (Note that the accepted answer is wrong.)
A: A Schwarzschild white hole should look just as black as a Schwarzschild black hole, since the gravitational time dilation factor and therefore redshifts are the same in both cases.
Just like it takes an infinite amount of coordinate time for everything to asymptotically reach a BH horizon, it should take as long for everything to leave a WH horizon.
For a WH you can just vertically flip the spacetime diagram of a BH, the outgoing rays are just as shapirodelayed as the ingoing ones.
