Most grout manufacturers offer a very wide range of color, and I would highly recommend that you try that first. Grout is made of sand and cement, and color can wash out very easily. Colors can fade over time, and I know that yellow, orange and red are the worst. Food coloring in the grout sounds like a recipe for disaster (pun intended). Worse, if you need to repair the job, how could you ever match the color again? As for concerns that the colored grout will affect the glass tile, have no fear. Glass is impervious and should not be affected. But when in doubt, test first.
If you really can’t find a grout color you like, your best bet is to have the grout colored at a paint store.