cast-iron stomach is a very strong stomach that can withstand bad food or anything nauseating

A person with a cast iron stomach can eat or drink anything without any ill effects Fig. a very strong stomach that can withstand bad food or anything nauseating. If I didn't have a cast-iron stomach, I couldn't eat this stuff. Fred—known for his cast-iron stomach—ate ten whole hot peppers.

It means that this person can eat any type of food without being sick.