Here's a simplified explanation of white it is important to use a white balance that is close to correct for the situation, and not wildly inappropriate or wildy inaccurate. Having the correct white balance set at the time of shooting gives the camera's demosaicing routines the right information to make the appropriate decisions to properly construct the color scheme that accurately represents the colors of the objects being photographed. Using red, green, and blue pixels, the camera must "estimate" the appropriate colors of objects and literally "create" the colors of every single object that the sensor can resolve. Keep in mind that the raw converter must create TWO OF THE COLORS at each photosite! If the white balance is wildly off, then the data being used is basically "bad data". Because a JPEG created by the camera is what the camera's histogram is created from, when the white balance at the time of shooting is wildly incorrect or inappropriate, there's a pretty good chance that the histogram will "lie to you", and you run the risk of blowing a channel as a result, or of not as fully exposing as possible. The camera should be set appropriately for the actual shooting environment--including the tone curve, degree of saturation, and the sharpening needed.
Several years ago, I had a Fuji S2 Pro camera. With it, I learned how incredibly beautiful digital photos could be---as long as a proper white balance was actually taken and entered into the camera. There is the widely accepted idea that the white balance can simply be forgotten about, and allowed to run in AUTO mode, and then later set "correctly" in post-processing. Most experienced or more technically-aware shooters will not agree with that idea, being well aware that the camera has to create color based on what it "thinks" the color temperature of the light was at the time of the exposure. When you get into artificial lighting that has weird and wild spectral deficiencies, shooting to a proper, real "valid" white balance is the accepted professional technique.
I'm not sure I agree with this. For one, the camera does not decide the colors when shooting in RAW. The RAW processor does, based on it's assigned inputs, so I'm not sure how, other than the histogram, it would lead to 'bad' data...and even if the data was 'bad', appropriate processing in a RAW converter would restore it to a normal picture file. I'll have to test this myself sometime tomorrow...set up a tripod, take a custom white balance, take a shot of a calibration card, and then set my white balance as far off as possible, take the same shot, and see if the results are identical after processing. I think they would be.
The other part I am not sure I agree with is that auto white balance is not accepted by experienced or technically-aware shooters. I would consider myself a very technically-aware shooter with quite a bit of experience and I think auto white balance is preferable to a custom white balance in many situations...to name a few, when your shutter speed is anything other than a multiple of 1/60th of a second under artificial lighting, when you are moving around your environment, when your shooting angles to the light sources is constantly changing, when several different light sources are in the picture, when shooting on a partially cloudy day when the sun is sometimes obscured by clouds...well, you get the point.
Sometimes, an auto white balance is more accurate than a custom white balance. Heck, that one is easy to prove. Set your shutter speed to 1/80th of a second and shoot a custom white balance or pick the flourescent preset...now take 5 shots under flourescent lighting. Now put your camera in auto white balance and take 5 shots again under the same lighting conditions. Auto White Balance will deliver more consistent results under circumstances like that.
Now, on the other hand, if I am shooting from a tripod, have some time, and want to guarantee my colors are perfect, I will take a custom white balance, and then use my calibration target to make sure my exposure is spot on. Takes an extra 30 seconds or so, but it guarantees me the perfect shot.
In any case, I feel like I am arguing both sides of the coin. The setting for your white balance matters, even when shooting RAW. There are benefits and cons to using auto or a custom white balance, but I think there is almost never a case where using one of the camera presets is a good choice.