Even when there is smoking in the room or house it can discolor.So unless the case is frequently exposed to sunlight like next to a window or someone is smoking in your house it shouldn't discolor at all. It also depends on the cases good quality plastics and metal. Check carefully in reviews or before buying the case.

Why does white cases turn yellow?

Clear phone cases are normally made from silicone—a polymer that's popular for its inexpensive and flexible properties. Unfortunately, these polymers turn yellow as they age. This natural process is accelerated when they are exposed to excessive amounts of chemicals, light and heat.

Do white PC builds get dirty?

Registered. They don't get that dirty easily but they do discolor overtime especially if they're plastic.