Single handle sink faucets: the three screw cartridge only mounts one way, so reversed hot and cold means the supply lines are crossed. Swap them under the sink.
Not sure this is your faucet? See how to identify your American Standard cartridge without a model number, or how to find your brand and model.
R120 family showers: install the back-to-back cartridge 952377-0070A, which is made for reversed supplies. The standard 023529 cannot be rotated to fix this. 952377-0070A back-to-back cartridge at Home Depot
Flash showers: pull the pin and manifold and rotate the cartridge 180 degrees so the UP marking faces down. See the shower guide.
Two handle faucets with the 994053: the cartridge is reversible. Move the clip and rotate the cam washer, or thread it in oriented for the other side.
American Standard pageIdentify your cartridgeStart hereWhen to call a plumber