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Rubbing alcohol can help as can enzyme based cleaners.

I often find that if something has mildewed, some really hot water and good detergent will work well.

Try hanging it out in the sun. Wash it as you usually would and then either hang outside on a line, or just drape it over something so that the stained part is in the full sun.

I do this with unbleached cotton diapers and it works great.

I'm not entirely sure if it will work as well on mildew stains but here's an old-fashioned trick that I've used to get rust stains out of linen that even a commercial rust-remover couldn't get out:
Make a thick paste of salt and lemon juice, slap it on the stains and lay out in the hot sunshine for a couple hours or all day if necessary. As the paste dries out squirt some more lemon juice on the paste to re-activate it. I've used this trick on white linen and it works wonders.

Hydrogen Peroxide kills mildew! You could also try an oxygen-based bleach, like Ecover. I have some beige outdoor curtains that get pretty dirty and I wash them with Ecover and it takes care of the stains without changing the fabric color.