You're using the dash light wire at the radio for its ground wire. When you plug the radio in, it is grounded by the correct ground wire in the wiring harness and / or the antenna cable, and that grounds out the dash light circuit causing the fuse to blow. Very few aftermarket radios use the car's original dash light wire or the tail light wire. On the original radio those circuits told the display to dim when you turn on the head lights and how much to dim when you adjust the dash lights. Either of those wires can be confused as the ground wire when searching for it with an ohm meter. They both read very low resistance, (like a ground wire), due to the many bulbs on those circuits.