Ideas for worn cherry kitchen cabinet door?Can I poly over old finish?

Any sanding will take away the stain color. I would try something like Old English Furniture Polish for either light or dark finishes. It has a stain in it that will color the chipped or scratched area to blend them in. If you cannot find Old English furniture polish, get a small can of stain, such as Minwax, that matches your cabinet and rub that over the worn area. Do not cover with polyurethane unless you intend to refinish the whole kitchen. It would make it stand out worse!

if the color is still there, often a light coat of clear oil finish will hide the bad area. Old English may work but if you need a heavily oil I would use Watco natural oil and wipe the whole face of the door with a light coat of oil and let dry.

This also works well where water has ate thru the lacquer finish around sink areas too!

Word of caution, don’t wrinkle up rags soaked in oil and throw away in the trash. Oil soaked rags can spontaneously combust building up heat being wrinkled up and start fires! Always lay used rags flat somewhere that can’t catch fire like the yard or middle of the garage floor and let dry completely then throw away safely

Check out this trick-it's like magic https://www.youtube.com/watch?v=Qf9M2D_Uc7Y