While you can't totally avoid your dishwasher-safe cups and Tupperware staying a bit drippy, there are some things you can do to help reduce the amount of hand-drying needed when it comes time to unload the dishwasher.
Consumer Reports recommends leaving space between all the dishes for improved airflow, increasing the temperature of the cycle if possible, and opening the dishwasher door slightly after the cycle has finished to let out excess steam and moisture. Compact Appliance also recommends skipping the quick cycle options and letting the machine run for its full wash and dry time, and using a rinse aid alongside your standard dishwasher detergent.
Rinse aids, including products like Jet Dry, are special chemicals that are dispersed through the machine to prevent water from beading on the dishes' surfaces, similar to a water repellant on a car's windshield.
Finally, the last practical way to keep non-plastic dishes dry is to empty the bottom shelf of your dishwasher first. Since most plastic dishes go on the top shelf — along with other cups that can catch water in concave bottoms — it's advisable to remove dishes from the bottom first so the puddled water doesn't drip or spill down onto them.
Maybe someday we'll all have dishwashers that are designed to actually accommodate the plastic dishes we love to use, but until that time take it easy on your machine when it doesn't get things 100% right. It's doing the best it can.