for the dawn and palmolive etc, as long as it's not liquid detergent it's ok.
liquid soap = good
liquid detergent = watch out!
while the liquid detergents will strip wax, they can/will also damage/strip your paint!!!
I typically use whatever inexpensive liquid soap is around.
I think it was 'dial' the last time I washed my truck.
I've used the blue corral too, it was given to me, seemed just like normal soap
I'm a cheap bastard, so it's usually the cheapest liquid soap...