Do you mean will the dye from the colored fabrics leach out and end up on the white fabrics?
We’re not laundry chemists so I really don’t know. I guess it depends on the type of fabric, the kind of dye, and the age/number of washings the items of clothing have had.
A brand new pair of dark blue jeans will lose more dye than a 2 year old green t-shirt that’s been washed 50 times.