I'm a 18 year cabinet maker and wood worker. That is classic water / moisture / humidity damage. The wood used in your cabinet doors shrink and expand with the seasons, temperature, humidity and in your case, salt air. Repeated cycles of this movement has cracked the top-coating on the wood and subsequently flaked off. Is the worst of the doors under your sink? Moisture from washing and cleaning with certain chemicals can also quicken the degradation.
Unfortunately, the damage is done, and there is no perfect solution to fixing it. Anything you put on it now has the possibility to make it look worse. Completely sanding and re-staining might be your best bet. Although if I were you, I'd take one of your doors off the cabinet, and take it to a Sherwin Williams store, or the like, and ask for some stain or color sealer that might look like an acceptable repair to you. Who knows, they may be able to recommend a local person who does this type of restoration.
For those of you who want to protect your cabinetry:
With RV's with all the moisture variables in which we camp, ( seasons, proximity to oceans, bodies of water, showers, cooking, dripping water, pets, must I go on) it would be a good idea to occasionally apply a conditioner such as this :
This is my favorite product. I find it works best to apply it to a microfiber rag, and gently wipe on sparingly. Old and dry woodwork could require a second coat. Be careful, as some surfaces in RV's are not real wood. Test in inconspicuous areas.
Good luck, let me know your thoughts, and outcome.