You can switch the accessory input on your head unit to an ignition wire that the remote start is currently powering. That will allow the head unit to turn on when the vehicle starts, but it won't work with the key in the ACC position any more. The other way to do it is to add another relay to the remote start system so that it activates the accessory circuit as well as the ignition circuits. If you tell us the remote start brand/model and the vehicle year/model, we can tell you how to do that.
Personally, I would rather the radio stays off when my vehicle is remote started. It's not like I'm going to be out there listening to it.