If the dye is not toxic (like the dyes you would use for coloring Easter eggs) it probably would be OK for your fish in low quantities. In most cases, too much of one thing is not very good. Your fish might not like swim around in, for example, extremely red water (and you wouldn't be able to see your fish very well too!!)

Sometimes ponds are colored to prevent overgrowth of algae that harm fish. The algae use up the oxygen in the water and so the fish don't have enough for themselves. The pond is dyed to filter out some of the sunlight to prevent algae from taking over. These dyes do not harm fish. However, I have not found any studies done on the long term effects of using these dyes in ponds. So it is possible it could be harming the pond ecosystem over time.