A dishwasher uses hot water and electrically powered spray arms that spray jets of water on dishes to remove caked-on food and grease. Even though a dishwasher's job is to clean dishes, it still needs to be cleaned regularly to prevent mineral buildup or old food from getting on your other dishes, which can stain them orange or other colors.
The primary reason that your dishes can turn orange in the dishwasher is orange pigment in foods such as sauces, bolognese and other tomato-based products. Plastic dishes are especially prone to staining and cannot always be cleaned adequately, which may lead to permanent staining.
Rust, which is present in many wells where rural residents get their water, can also turn your dishes orange both when washed by hand and inside the dishwasher. Rust is not necessarily dangerous but can be bothersome and also affect the taste of drinking water.
Scrape off excess food from your dishes before placing them inside the dishwasher. You don't necessarily have to rinse them off completely since that is the job of the dishwasher but don't put food inside with half-eaten tomato slices or chunks of tomato from a sauce. If your water has a high rust makeup, switch to glass dishes if possible, as these are less likely to stain.
Once your dishes have already been stained you can try to salvage them so you don't need to purchase replacements. Place plastic dishes in direct sunlight, which acts like bleach. You can also wash the dishes by hand and add a small amount of bleach to the water. If the orange buildup is inside your dishwasher, run a full cycle with nothing in it but a bowl full of plain white vinegar.