I've heard estimates that a tenth of stringed instrument players are "rusters." It's not really rust, of course, but the strings respond to something in the body chemistry. I assume you've tried the obvious (different string chemistries, e.g. phos bronze instead of nickel steel, or vice versa).

I'm not a ruster, so I can't comment from personal experience. I've never heard of something you can eat that helps (which doesn't mean there isn't anything, of course). But you can try dipping your fingers in baking soda before playing, or a very light coating of grease. Or maybe wipe the strings and then wipe again with a baking soda cloth after playing, to neutralize the chemicals.

Also, if you're a fingerpicker, consider Alaska Piks. (Yes, that's how it's spelled.) Unlike regular finger picks, they are designed to fit like ordinary fingernails rather than as anti-fingernails. So you don't contact the strings as much. It isn't much help -- the real problem is your fretting hand, not your picking hand -- but it's something.

I am sure that if you start searching for "rusters," you'll find more ideas.