Do that many people rely on the white for the cross? I was wondering this, as since I started speedcubing I have been colour neutral, and looked for the side with the best cross, although this is a disadvantage in that if there isn't a good cross, it really holds my time back.
I've only been cubing for a few months now and I've found it easier for color recognition while learning the F2L, OLL (still learning), and PLL. From what I've read on this and other sites there's a trade-off for both being color neutral and sticking with just one color. I decided to follow the crowd and begin my learning tract with the same color as most everyone else. Within the last couple of days I'm shifting to learning the x-cross and yellow crosses... very similar to the white cross but the colors are flipped R/ L. I don't think I'll be 100% neutral but I'll try anything to help me learn the x-cross easier.
What method are you using to complete the first two layers? LBL? Fridrich? I use Fridrich and have found that learing the F2L was easier when I was looking for the same colors over... and over... and over...
The only thing I have read for a recommendation is to pick one color for a cross and stick with it while you learn.