Driving a RGB Led strip with a RGBW controller
Just use 3 diodes to pull the R, G, B lines LOW when the white channel turns on.  I'm going to assume that your LED strips run from a 12V rail.  Because the voltage drop across the resistors inside the strip is fairly small, I'd suggest using Schottky diodes.  MBR140 is good for 1 Amp continuous but you may need larger diodes depending upon how much your channel current is.

Simply connect the cathodes of all 3 diodes together and to the (W) output of your controller, connect each of the anodes to the same point as the R, G, B outputs of your controller.