Cotton and most other fibers do not start life WHITE. They are usually some shade of off-white or beige. The first step in making them WHITE is to wash (scour) it, the second step would be to bleach it and the last step, dye it with Optic whiteners.

All fabrics are washed, some are bleached and some are both bleached and optically whitened. In the industry, fabric to be dyed is not usually optically whitened because the optic whitener is like a white dye and occupies the same molecular space that the colored dye should occupy. Some fabrics are treated with Bluing agents to make them look whiter. Both whitened and non-whitened fabrics can be various "shades of white" so you may see perfectly dyeable fabrics and garments that are greyish, ivory, bluish or other tones that are not exactly paper white. This is the nature of white fabrics. 

In our experience we can't tell the difference in the color of dyed fabric which had or had not been optically whitened. But that's just us. We offer fabrics that have and have not been bleached and or optically whitened. They all dye just fine. Your job is to add the color!