Mild soap and water
The best solution is a mild dish soap (or similar)-no Comet or abrasive type soaps-and scrub with a plastic kitchen scrub pad-NOT steel wool.. Mildew is almost impossible to remove completely, and even when someone SailCare does it, the mildew stains often return. You can usually get SOME of the mildew, but rarely all of it.
Most other soaps will damage the resin, threads, etc.
Also, doing the "re-resin" thinking is, IMHO, a total scam. Once the original resin has broken down, and the dacron itself has stretched beyong its' ability to recover, the fabric can never be rejuvinated. By adding more resin, you add weight (bad), but the resin is now doing ALL of the shape holding-and that "shape" is already distorted; no longer a useable shape. Finally the new resin breaks down very quickly, and the effects (which again-do NOT include changing/improving the blown out material) are nil. All you are doing is getting the sail to hold it's already ruined shape for another season.
If you really want to get another year or 2 from a blown out sail, and want to spend some money doing it, you will be MUCH better served by having the sailmaker do a recut. He can cut away the worst parts of the sail (near the outside edges) digging into "fresher" fabric, and removing some of the"hook" in the leech (if there is some). He/she can re-shape the luff curve to some degree, which will again yield SOME improvement. You will lose a small amount of sail area, but the improvement, however small, will be better and longer lasting than what you would get from reconditioning.
If this is what you are considering, take the amount quoted by the reconditioner, and use that # as a limit (more or less) for the amount you are willing to spend on a recut. So, if they want $500 for re-resin, tell the sailmaker your "cap" on a recut is $500. Spending more than this is wasted $$.
Personally, I might go for a minor recut BEFORE the sail is completely shot, and after that, rather than spending more on a dead sail, put the $ in the new sail budget, and when the time comes to replace, you will have some of the costs "covered". No reason to throw away good $$.
My opinion is that the people who think they have had good results from reconditioning were doing this to sails that still had some life in them anyway, and likley did not need this. The biggest thing you gain is "weight aloft"-not very
Not that I have an opinion!!