"non-(banana republic)", not "(non-banana) republic".

Then you have to write "non-banana-republic". "Non-banana republic" is not even ambiguous, it's just wrong.

So then it does indeed fit into the non-(banana republic) category :P

But that's not what you wrote. "Non-banana republic" can only be parsed as [non-banana] republic. You need to write "non-banana-republic" if you want to say non-[banana republix]. Better yet, use a less clumsy turn of phrase. Best of all: drop the remark entirely, it's pointless.

"non-banana republic"

I think Camillo is trying to point out that the UK is not a republic (banana or otherwise) but a Constitutional Monarchy.