I have red and black hair and I wash my hair everyday. And so far I haven't noticed my hair color changed.
Other shampoos I've used on my colored hair made my red fade in like 5 days. It's been 2 weeks since I colored my hair and it's still looking good!!
My hair is colored darker than natural and I haven't had any issues. The product itself has sort of a yellow tint (I assume from oils- think cocoa butter yellow.) which could *possibly* cause issues but I doubt it honestly.