I rinse my sails when I think that I need to. I never put them away wet/damp although I see the point that salty sails are never truly dry. When it got to the point where you could scrape the salt off the sail then I would take it home and hang it up and rinse it. I rinsed my new sail before I stored it for a couple months. I hope that it was dry enough (it is nice, new and WHITE!)
As for gear- it gets rinsed each and every time. The boat too unless I am toolazy to go up and turn on the water or the hose is broken.