How about CLR, Lime Away, etc.? I know they'll eliminate the rust stain - what I don't know is if they'll bleach the fabric. Even if they don't bleach the fabric, would there be any color left in it after removal of rust stains by any means? I have some Lime Away which contains Sulfamic Acid. I'll test it on a piece of cotton web gear and let you know. I have a piece of WWII-era web strapping around here somewhere which would be a good test with the dyes of the period.
ETA: Couldn't find the strapping but I tested an old greenish/khaki bandoleer - no effect on the color or material.