1) Pull the post because it will look better. There's no way to scribe that 100% the first time. Plus, with wood movement, even if you were 100%, once your molding shrinks, you'll be left with a nice gap anyway. Tell your client that. Cut the post to fit the cabinet.
2) Or use a tool like the multimaster to cut a relief in the post. Chisel out the rest, and tuck your board in behind. It's kind of a bit of both worlds - little bit of cut the post, little bit of scribe.