The colors of the fabric dyes may not affect the drying time much, especially when the dyes come from the same company.

Factors that can affect drying time much more include the amount of dye used, the area of the fabric, the temperature of the dye bath, the ambient temperature (for dyes that need to sit after they have been applied to the fabric), the degree of air circulation, the type of fabric, and how the fabric was processed in the factory. If all these factors are equal for two pieces of fabric, and only the color of the dyes differs - blue vs. red, for instance (not light pink vs. dark pink because that may change the amount of dye) - then you may not see a substantial difference between the drying times of the two dyes. You can test this idea by using two different colors of tie-dye.

You should do the experiment yourself and find out!

I predict that dark fabric in the sun will dry faster because the dark color will absorb more light and so evaporate the water faster.

I predict that dark fabric in the shade will dry slower because the dark color will radiate away more heat and so the fabric will be cooler and evaporate more slowly.

I predict that the humidity and temperature of the air on the day that you do the experiment will have a larger effect on drying time than the color of the fabric would.

I recommend you to think about what you could do to determine the effect and ask questions on parts of the cientific method that you should review. You might consider what the "drying" process entails, the factors which affect the steps of that process, and how color might influence those factors.

I don't think color would affect drying time unless the fabric was dried in the sun, where the different colors would absorb different wavelengths of sunlight.

Here's an answer from a google search of your question:
How Does Color Affect Drying Time? | Science project | Education.com science projects

1. In this experiment, it is expected that red, yellow, and orange colored garments will dry faster because these garments absorb high energy, high frequency wavelengths of light that will raise the temperature of the garment and increase the rate of drying.