Here's an experiment for you, Larry.
Play a simple progression where it 'belongs' on the guitar. G-C-D.
Tune the guitar down a half step and repeat using the same finger positions. (Maybe on a different day?)
Does it bother you the way playing with a capo does?
Then capo up one fret while still tuned low, and repeat. Now the pitch is back where it should be. Is this okay, or is there still something 'wrong'?
My hunch is that your problem with a capo is that your fingers are saying G, G, but there's A, A, in your ears.