Any liquid with a dye or colouring in it will stain to a certain extent. There are so many variables.... the colour of the clothing material, the length of time the dye is allowed to sit in the cloth, if it's allowed to dry, the quality, type and density of the fibres in the cloth etc etc. Also remember that paintballs impact at a fair speed. This will have the effect of injecting any dye compounds into the cloth fibers.
Also the detergent you first wash it with, the temperature you wash at, whether you tumble dry or not can all make a difference to whether the dye fixes in the cloth.
A good last resort for stubborn stains is dabbing or wetting with Acetone (nail polish remover- check there's no additives though, pure acetone is best) as this will dissolve most synthetic dyes and is also good at shifting organic compounds. Don't use it on your goggles or shades though! Test on an inconspicuous area first though as it may also shift the dye or colour of the cloth. You can also try both bio and non-bio washing powders.
I agree that paint that stains goggles and sunglasses would be bad, but I'd have to see evidence first hand, as it would have to contain reasonably powerful solvents to melt plastic material or coatings.
If it's a hot day and you're worried, wipe your shirts off with a damp cloth straight after the game.
Alternatively, wear your stains with pride!
P.S. For the record, I have been shot (a lot!) with Pink Zap Chronic at our training days and the paint washes out fine.
