It's probably not so much the shampoo as it is the water that's affecting your hair color. I have actually inquired at a lot of different companies, and most of the shampoos do not affect your hair color. What happens is this: When you color your hair, the hair can become more porous. And that means that everything you do to your hair can affect it more. So sun exposure will make your hair more brassy and more dry. The sun takes the water out of your hair, and ultraviolet rays can change the color.
The sun also dries out your skin. So that's something you want to be careful about.
Don't stay in the shower for too long and don't let the water just run over your hair for more than 10 minutes at a time. Use a conditioner and a shampoo that are specifically designed for color-treated hair, because they will coat the hair and give it some strength and volume. That helps protect the color from fading over time. But it's more the water than the shampoo that's stripping your hair of color.
WebMD Ask the Dermatologist.