I moved from Texas to Georgia, where a front license plate is not required. So I left my front Texas plate on while sporting a Georgia plate on the back. Visiting New Jersey got me some strange looks.
In most cases it probably had nothing to do with the different plates. NJ is a strange place. Strange people tend to look at people strangely.
(only half joking) New York, where I am, is even more strange. But in a different sort of way.