Subject. I do care about eyes (ish), so I have the "Night light" setting enabled almost always (Windows and android). But when I edit photos, I tempted to reduce color temp on them, and results looks cold for other people. How to keep the right color balance?
"Night Light" or "redshift" or other night light color apps don't do anything (as far as I know) to protect your eyes. Their intended function is to protect your sleep -- blue light is a signal to your system to remain awake. By reducing it for an hour or so before bedtime, the theory is that you'll find it easier to drop off to sleep promptly on hitting the pillow.
What I'd recommend in this regard is to disable your "night light" setting for photo editing, but then stop editing and turn the night light back on (or better yet, just get away from the screen, perhaps read a paper book) an hour before bed time. This will let you see the colors of your images accurately, and still protect your sleep.
TLDR: Turn Night Light off. Calibrate your monitor with a colorimeter.
How to keep right color temperature if I edit photos with night light mode turned on?
Normally, you can't because the intensity of Night Light/Shift, in some implementations, varies with the time of day.
I have the "Night light" setting enabled almost always ...
If the effect is constant on your devices, you can create an adjustment layer that makes the image look right to you. Then remove it before saving. Use the same adjustment layer for all images.
You can also use the dropper tools to check the color values of areas that are supposed to be neutral.
Turning Night Light off only when editing images is inadequate because your eyes/brain takes time to adjust. Your edits will likely be inconsistent over the course of each session and across sessions.
I do care about eyes (ish) ...
As Zeiss Ikon has stated, Night Light does not protect your eyes. It is intended to affect sleep. However, since you are able to adjust images to look right even though Night Light is turned on, blue light is being allowed through. So whether Night Light can improve sleep is questionable.
If you have sleep issues associated with light, you need to stop using all artificial light at sunset. If that is not possible, you can use amber safety glasses. Clear computer glasses that claim to "block" blue light, but obviously don't, are useless.
... results looks cold for other people.
If you care about what images look like to other people, don't use Night Light. Also, calibrate your monitors with a colorimeter.
The major problem with "night mode" probably is that it's by no means standardized. What you did not talk about is the ambient light: Do you edit in complete darkness? If so, the color temperature of your display "white" would adjust your visual system to white (within limits). However if you have an ambient light, the whole situation is much more complicated: Ambient light also infuences the "white point" if it's relatively strong.
You basic problem is: Your images will look the same only under the same viewing conditions, that is: Same device, same mode, same ambient light.
Easiest solution: Realize that it was a bad idea to adjust the photos in that way and then share them.
My short recommendation is "do not do that", or even better, "consider your priorities". Different settings are good for different purposes.
I think a good analogy here would be trying to use rubber boots for running. Rubber boots are great when you are walking through mud (like night mode for doing something where colour reproduction is not critical, like reading StackExchange at night) but do a horrible job when used for running (editing photographs).
Simply put, you should calibrate your display for working on photographs and switch to night mode when doing something else, especially at night. And if you can avoid it, do not edit photos about an hour before going to bed.
If changes to color temperature are problematic in night mode, avoid changing color temperature in night mode. The best way is to get color temperature right — by “right” I mean the way you want it — in camera.
Getting color temperature right in the camera means there’s nothing to fix later on the computer. More important it means knowing the color temperature does not need fixing despite what your eyes tell you...and eventually your eyes will stop telling you the color is wrong.
Most cameras allow setting a custom white balance and there are white balance targets that fit in camera bags. Some will even fit in a shirt pocket.
Sure I am making it sound easier than it is in practice to slow down before making the pictures we all want to make. But in the long run getting it right in camera is easier than fixing things later. And taking as good a picture as you can is easier when you fully commit to taking as good a picture as you can while making the picture.