Schosche makes an adapter cable to allow connecting an aftermarket receiver to the Ford speakers using the Ford speaker cables/connector without cutting. It bypasses the factory amp. Scosche P/N FD02. I bought mine at Walmart for about $7.00.
Just disconnect the rectangular connector (the one with 8 terminals) from the factory amp - plug in the Scosche connector to this connector - connect your new receiver's speaker output wires to the Scosche wires. That's it. The small rectangular connector/cable going to the factory amp is not used.