It's no surprise if the navy fades, as it is a notoriously unstable dye. As for red, red is a loose dye which means that there is always loads of runoff in the wash. Never, ever put a red garment in with whites unless you want them pink!
Turning garments inside out is fine, as long as you don't have any real dirt on them: grass, food stains, etc. Then you can try spot cleaning the heavily soiled area and then turning it inside out. Also, if you have a front load washer, you don't need to turn it inside out. Turning inside out is only to prevent surface abrasion from the agitators in top load washing machines. It probably wont affect dye run-off, or how the fabric reacts to the oxyclean, chlorox or chlorox 2. You all should also be aware that most water purification involves the addition of chlorine to public water supplies, so there is always an amount of bleaching involved in washing. That's why many people don't wash their jeans if they have special whiskered finishes, etc. and instead have them dry cleaned. Dry cleaning will preserve colors the longest.