Who makes a peel and water proof LED strip lights that can be cut?

Try a hobby store. My husband lights up emote control planes with them.

Menards carries them. Or try Home Depot or Lowes if you don't have Menards in your area.

https://smile.amazon.com/gp/product/B06Y2WC8LM/ref=oh_aui_search_detailpage?ie=UTF8&psc=1

These are pretty fun, with some basic wiring you can do your cabinets. Only problem is the only control for it is the remote, probably need some good adhesive in addition to the pull and stick....I saw a 4 pack of mini LED tap lights at SAM's club-zero wiring required...Also other led options all over Amazon.

I found mine on Ebay. Some are multi colored and others are white. Some have a lot of options ranging from remotes to blinking and so on. I used pure whites with remote (for adjusting the brightness) under my cabinets in the kitchen. Ebay is usually the cheapest. If you can plug in a plug then your set. Were ever you intend to use them you might want to get the water proof ones.

If you want waterproof LED check out Kistler. They have a clear cover that snaps over the strip.