Hi,
I agree with Matthew that color is arbitrary. All those things are not visible with the naked eye (at least not with colours). And some types of photography such as narrow-band are false color by definition.
However let's assume that you define "correct" color as "what the eye would see if I were really close the subject and able to perceive color of really faint light sources as well as color from intense ones".
The key facts that allow us to answer this question is our eyes are evolved to see in daylight (colors are very different if you use a tungsten light or a blue LED or moonlight for example, this, the light source is known as the "white reference"
. Also, that our eyes lose the ability to see colour in the dark, and they are less sensitive to red to begin with (red suffers most). This is why when you take a photo in a dimly lit room things look too red: the sensor is not wrong. It is your eye that cannot see all this red.
In a nutshell:
Things generally tend to be much redder (or shifted to red, e.g. pink, purple, orange)) than we have in mind. Especially where there is a lot of dust and stars. Excluding influences from nebulae (such as the Pleiades that are very blue), the general, default color of the deep space background is shades of red and orange. When the sky background is shifted to blue or green, this is usually for reasons closer at home: airglow, zodiacal light, moonlight, artificial light pollution. And it can only be pitch black where you have a really dense dark nebula obscuring the background, such as the coalsack.
Now, to get "correct" colors with sunlight as the white reference, you need to calibrate. You can use Astropixel Processor which uses a statistical model to restore star colors so that they match their expected distribution, or the more advanced Photometric Color Calibration of PixInsight. This solves the image, finds stars with known colors and makes necessary adjustments so that they look they way you would expect, given a known white reference. If you want sunlight as your white reference, use G2V star. If you want Rigel-light to be your white reference, use B8 star. If you are shooting a galaxy (a heterogeneous light source), it is probably best to use the "Average Spiral Galaxy" white reference.
Or you can process your photos non-linearly from the beginning, using a known white reference (preferably Daylight). This is actually a good idea if you are using a DSLR and do not have much light pollution.
Please see this discussion for more details. It is truly a huge subject:
https://clarkvision.com/articles/color.of.the.night.sky/
