I have the same problem - with my backsplash. I have to grout colorant, but I haven't tried it yet.

If it's a cement based grout there are many variables that will come into play, there are new grouts available that don't have the issues of old cement based grouts, splotchy, stained, moldy wet grout can be a thing of the past with single component grouts .. typically removing and re grouting is one option, a colorant is another, they work quite well.

With any cement grout, different water amounts will cause color variation. If you have hard water this too will discolor the surface of the grout. To fix discoloration from hard water minerals simply etch the surface of the grout with a knife or flat head screwdriver.

The main problem I see with grout colorants is that when cured/dried they tend to have a sheen. If your tile has a matte finish the grout lines could stick out like a sore thumb. I have heard of people staining their grout, as the stain soaks into the grout better than the colorant and does not leave a sheen. I have yet to try this so I am not sure of the outcome over a period of time.

Has anyone ever tried Grout Shield color enhancer? I have seen this online but haven't heard how well it works.

Use Prism grout.

The bathroom has already been grouted, and the contractor didn't mix it correctly or something went wrong because after it tried, the greys are different shades and when it gets wet- the grout darkens and then it dries but is still various shades of grey. Does prism grout have a color stain, or enhancer that could maybe darken it all enough to even the grout color out?

Prism grout stays true to color and it's what our tile guy recommends. They don't have a huge variety of colors to choose from, but what they do have stays true to color. Next time!