This ability doesn't overwrite any previous colors. Rather, it adds another color.

If something affected by Indigo Faerie's ability is normally colorless, it will simply be blue. It won't be both blue and colorless.

After Indigo Faerie's ability resolves, an effect that changes the affected permanent's colors will overwrite Indigo Faerie's effect. For example, if Indigo Faerie's ability is activated on Llanowar Elves, the Elves will be blue and green; if Aphotic Wisps is then cast on the same creature, it'll be just black.