For designers and photographers, color management is even more important, and there is a lot of debate surrounding the best options to use. Photoshop, for example, has a million and one different color settings (or, you know, at least a handful). This article is very helpful for explaining exactly what they are and how to set them up.
The bottom line? At this point, it’s practically impossible to expect colors to display identical for all users, regardless of what type of equipment they use. If colors are displaying drastically different for you all of the time, like images that should be grayscale have a bluish tinge, check into calibrating your display. If you’re a designer struggling with color inconsistency, read up on color settings and how to properly set them in your editing software.