I have a G&L tribute legacy which has rust on the tremolo and pickup magnets. What's the best and safest way to clean this? Product recommendations would be greatly appreciated.
Remove the strings and gently rub the poles with a pink pencil eraser. Use a real rubber eraser, not one of those shītty plastic ones that come on soft pencils. You won’t be able to remove it all, but get what you can.

You can take the trem apart and clean it piece-by-piece. If the metal on metal bolts/screws are stuck use a little liquid wrench to loosen them. Take the bridge apart, sorting the parts into individual bowls as you go. Scrub off rust with a toothbrush and steel wool in warm soapy water. As soon as a part is clean rinse the water off with rubbing alcohol and dry it or it will rust again.

Do your cleaning in a kītchen strainer inside of a bucket; not anywhere near a sink. You don’t want parts going down the drain! Take setup measurements and close-up photos of the saddles and bridge before you start to save time when you have to put it back together.
You can also dip the rusty bits in some CLR

In Canada, it's C, eh? L, eh? R, eh?
Sounds good...EH!

The part that has me worried the most is the pickup magnets. I'm thinking some CLR on a rag and gently try and get the rust gone that way.
Once you get it cleaned up, start washing your hands PRIOR to playing, THEN wiping your guitar clean afterward. This will go a long way into protecting your baby.
--- Joe ---
77 Bradley LPC || 07 PRS CE22 || 11 PRS MC58 Artist || 95/02 Fender Strat || 99 Gibson LP DC Std Lite
06 Ovation Elite-T || 12 Martin GPCPA4
Boss GT100 || Peavey Stereo Chorus 400 || Peavey Bandit 75 || Roland JC77
Would there be any danger in removing the tremolo and putting the entire thing in a vinegar bath to remove the rust? I'd then take it and dry it properly and reinstall. Should it need to have the setup redone after that?
You'd probably have to redo your setup.

Before you get too deeply into this, get StewMac on the phone and ask them for suggestions.

I realize this is closing the barn door after the horse is gone, but I keep telling people to put a VCI in their cases. A VCI is a Vapor Corrosion Inhibitor. You can find them at places like theruststore.com. I toss the little canister ones in the case and swap them out every year and a half or so. I'm sure you've seen the VCI wraps and bags for tools, parts and whole assemblies; this is similar. It actually emits a vapor that puts an anti-corrosion coating a few molecules thick on the guitar. You can't see it, feel it (and it's harmless to painted surfaces), but it's helping to reduce corrosion on things like trems, pickup coil wire, etc.