This is something I struggle to correct in myself. I was brought up with a bit of this 'no slouching at the table', but not enough, so I suspect I will have to spend a long time consciously reminding myself not to slouch. In some other ways I have stiff manners, coming from quite English and German stock. For instance people will sometimes apologize after touching me (not as in bumping into me, but in the way people will touch you during conversation, perhaps on the forearm, knee, or shoulder), apparently because of a subtle negative reaction I give off.
I've mentioned a book I'm in the middle of on education in the middle ages. It was held as axiomatic that bodily discipline - a noble posture, smooth and controlled movements, and so on - contributed to moral formation. I can see a lot of sense in this idea, though it goes without saying that one shouldn't exaggerate it.