That was going on in my car when I bought it. The previous owner had swapped in an aftermarket head unit and every time I would start the car with the radio on it would pop and my dog would nearly jump out the window.
My solution was to buy an OEM Ford unit and toss the aftermarket in the trash.
If I were you I'd call tech support for the unit to see if they can work out a solution for you. If not then send it back.
2005 4.0 MT dual exhaust GT mufflers GT suspension and wheels