Virtual fermions vs exclusion principle

Any pair of Fermions that try to get into the same state in a Feyman diagram are cancelled by a contribution from another diagram. The factor of (-1) from closed fermion loops ensures that this happens. It also shows why Feynman's original idea that there was only one electron in the universe that was busily going forwards in time as an electron, and backwards in time as a positron, does not work. You need the closed virtual loops to do the cancellation and ensure that the Pauli principle is satisfied.