If a recipe calls for 2 1/2 cups of shredded chicken, is that the same as 20 ounces? I'm always confused when it comes to dry ingredient measurements in recipes. Can I simply just convert each cup to 8 ounces?
In general you can't convert volume measures (like cups) into mass measures (like ounces) without taking into account the specific thing you're measuring, because different substances will have different densities in a cup.
If you search online you can find conversions for different common food items but these vary. The website CookItSimply provides a conversion for cooked chopped chicken as 1 cup to 4.4oz; the website FreeFoodTips gives 5.22oz; TraditionalOven.com gives 4.94oz. Note that these are cooked weights, and chicken changes weight as it's cooked.
However, a recipe that incorporates shredded chicken isn't likely to be very sensitive to the exact quantity so I would take the recipe as just giving an indication of the rough amount of chicken to use: think of the amount that would fit in 2.5 cups and go for roughly that amount.
Conversion from volume to weight or vice-versa is different for all foods, so there is no standard rule. One cup to eight ounces only works for foods with the same density as water (it is a reasonable approximation for most liquids e.g. vinegar, milk, wine).
http://www.kingarthurflour.com/ has a printable chart of dozens of foods and weights of different amounts in ounces.