What I have used successfully to remove rust stains from sails is "The Works" which will set you back a whopping $1.00 at your local Dollar Tree store.
http://www.dollartree.com/The-Works-16-oz-Tub-Shower-Cleaner/p6065/index.pro
The oxalic acid in its formulation is what converts/removes rust stains.
I have never seen any evidence of damage to my dacron sail fabric (which is a plastic variation afterall). No evidence of adverse effect even many years on. Reference to damage to sails from solvents and cleaners might pertain to newer sails that still have their protective coatings on them. (This is just my opinion.) But many years on, probably not much of the coatings are still left to damage.
Depending on the severity of the stains, several applications will be needed. More of the stain will disappear after each application.
Going forward, you might want to determine what has caused the staining in the past. Most often, its that the sail comes in long-term contact with stainless steel fittings or riggings that have developed surface rust. Most on this site who have used it (including me) are very pleased with a product called Spotless Stainless that removes rust and the re-passivates the surface to slow down the rate of future rusting. Do a forum search for Spotless Stainless. You will see many before and after pictures. Great to use round a new old boat which most likely will have rust splotches on many SS fittings.
Back to "The Works": The stuff also does wonders to remove tannin and rust stains from gelcoat. Here is picture of it's effect on my hull under my transom overhang. The picture was after only one application. The second application re-stored the gelcoat to full white.
Note: Whoops -- after writing this, I decided to look at your profile (sail101e). Probably the Spotless Stainless info about not much use on your boats. Any, "The Works" should help out your sails. And rust/tannin stains you might have on your hull and deck.