No it is not subjective: Correct white balance means that a white, gray, black or full gray scale surface is displayed without discoloration and have the same RGB values from the whitest down to black and .
One should distinguish between the use of gray cards that are more suited for exposure and a card where the white balance should be made towards a value around R 220 G 220 B220 and that the card has such metamerism characteristics that a white balance can be made in different color temperatures.
Then that the image results do not fit is a subjective evaluation .
Great response from Mikael. Too many people just glibly talk about a "grey card" for white balance. They go on eBay, buy a $5 piece of grey cardboard, try to use that to do white balance, and end up with something that looks really dreadful. While this grey pieces of garbage may be fine for setting exposure because they are the middle tone that the meter expects, they are often times dreadfully bad for setting white balance.
Do use such an aid for white balance, it needs to be something that is specifically manufuactured for that purpose. I use the Lastolite EZBalance. It has the benefit of being perfectly suited for both exposure and white balance. Personally, I do a custom in camera white balance by shooting and image of the EZBalance filling the frame, and then using the custom white balance functions of the camera to adjust according to that image.
Even if shooting raw you need to worry about this. The camera will apply some sort of white balance adjustment to your raw file, whether you want it to or not. That's what all of the Tungsten, Daylight, Shade, Cloudy, Flourescent, Auto White Balance, etc etc settings on the camera do. And while those can be close, they won't be perfectly neutral. And it takes a very finally trained and perceptive eye to be able to look at one of these images on the screen and know with percision how much Temperature and Tint to adjust to get it back to neutral.
By setting the camera white balance to a custom level by shooting my EZBalance, every image I take that comes off the camera down to Lightroom has whites, greys and blacks that are balanced - equal amounts of Red, Green, Blue. From there I can cool it down or warm it up for taste, but I'm not having to make large adjustments for correction.
Get that white balance nailed and you'll reduce your post processing work flow by a huge amount.