The reason that cast iron cookware should not be washed in the dishwasher is the dishwasher and harsh detergent in the dishwasher can cause your cast iron cookware to rust out.
When you wash cast iron cookware in the dishwasher the seasoning of the cast iron cookware as well as the protective, non-stick layer of baked-in oil and lard will be removed from the cast iron cookware.
Always gently wash cast iron cookware by hand and do not do any harsh scrubbing as it will remove the seasoning on the cast iron cookware and cause it to rust.
You can just rinse the cast iron pan to remove any food residue from the cast iron pan or use a paper towel to gently wipe down the cast iron pan and use just a bit of soap but not too much soap as it can remove the baked in oil.