Try and save the cabinets or not?

If all the cabinets are salvageable, seems like it would be ok for them to be different. But it's probably a personal matter of what is important to you. I just normally don't throw away anything that is still useful.
What's your flooring going to look like?

Was the wood very dark when you put shellac on it? Recreating the rounded corners out of solid wood would be difficult.

I think you can save the cabinets but they look discolored? Or is that just dirt? You can also bleach darkened spots with Deck Wash. Paint on, wait to see how it's working, paint some more... I usually sand a little bit first.

My vote is save the cabinets.

Did your upper cabinet to the left of/over the sink have a cutout for a water tank spigot?

I would say save.

Before making any final decision, I'd try rubbing all of the woodwork down with denatured alcohol..over and over again. It is almost always shellac. Sometimes this removes dirt and grime, and the old shellac kind of melts into a slurry that you can spread around, ending up with a pretty nice result. Then, you can apply a couple of fresh coats of clear shellac over it to freshen it up. If it doesn't work, all you've lost is a few $ worth of solvent and some time.