Removing Rust From Detergent Dispenser on Washer?

First check to make sure you are really dealing with rust and not a build-up of detergent residue or water impurities. Vinegar usually gets rid of those quite safely.

If you have real rust, which is actually quite rare, you can convert it to gray iron-phosphate by using phosphoric acid.
Phosphoric acid is quite safe. Many soft drinks, like CocaCola, use it to provide the illusion of tartness in spite of the heavy load of sugar. If you can't get Phosphoric acid, you can pour CocaCola or similar soft drinks, that contain it, through it until the brown rust has turned battleship gray.

Iron Phoshate is actually a salt crystal, and will not degrade any further. It has gone as far as it will go.

You can also buy "Naval Jelly" at the hardware store. That is jellied phosphoric acid and won't run off. That is handy for some places. Both liquid and jellied clean up with water.

Have FUN!
DearWebby
webby.com/humor