As far as strong bases vs strong acids and their reactivity with other substances, it depends entirely on the chemical, it's concentration, and the material it's in contact with. Lye will react with the zinc that is in brass. Any oxidation from getting it on inlays or patchboxes should be removable.
The iron nitrate that Kibler sells is not highly acidic. It's really just a solution of iron nitrate in water. The term aqua fortis actually refers to nitric acid, which is a strong acid and extremely corrosive to many substances. So, Kibler's iron nitrate solution does not need to be neutralized. If you put it into inlets, it's possible it can promote corrosion to metal parts in there because of the iron ions that are in the wood in contact with the metal. Not because it is strongly acidic, because it's not.