Perhaps the most authentic way to age muslin fabric is to hand a length of it to a pair of 9-year-old boys and ask them to go play World War II, using the muslin to make an army tent in the woods. One good rainstorm and a couple of dew be drenched mornings later, you will have a fine piece of aged muslin.
If you need a more practical aging method, there's another option: natural dyes.
Chances are, you have a natural dye already in your kitchen. Tea gives muslin a warm brown color, coffee a deeper brown, and yellow onion skins impart a lighter golden tan. Any of these can produce a nice antique look on muslin fabric.
Prewash the muslin to remove sizing and prepare it to take the dye.
Prepare the dye. For coffee and tea, simply brew it to the intensity that you want. Onion skins need to be boiled for about 15 minutes. Unless you want to add character with splotches of uneven dye, strain the "onion soup" and use only the liquid. Add roughly ¼ teaspoon salt for each gallon of dye.
Completely submerge the evenly-damp muslin in the dye bath. If you desire a uniform color in your finished project, it is important to regularly stir or agitate the fabric. Do not pack the muslin too tightly into the pot or tub. The dye needs room to mix if you want it to be absorbed evenly.
Rinse thoroughly in cool water. Do not wring.
Hang to air-dry. Drying outdoors in sunlight may further enhance the realism of the aging, but you will need to allow for some fading of the color. Hanging the muslin indoors or in the shade will reduce fading, but expect the color to lighten as it dries. If you want a softer feel to your fabric, hang the fabric until all dripping has stopped. Then finish by machine drying on low heat with a fabric softening dryer sheet
Muslin is 100% cotton fiber. Expect some shrinkage. For the longest lasting color retention, dye your fabric in a large pot on the stovetop. Warm your dye bath with the muslin in it to about 120°F and hold the temperature there for at least 20 minutes, stirring occasionally. Allow to cool, still stirring occasionally. If you have larger lengths of fabric that must be dyed in the washing machine, use the hottest tap water in the wash cycle; allow it to cool somewhat before continuing with a cool rinse. The natural cuticle of cotton fiber is temperature sensitive. The warmth opens it and allows it to absorb dye better, then the cooling closes it to help lock the color in.