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White balance is measured in neutral tones. Changes in colors relative to each other in the Color Checker are more accurately termed "Selective Color" changes.
For example. This is what the color checker should look like if reproduced exactly, per the RGB values in the documentation...
Here's what it looks like when shot with R=G=B neutral White Balance with different "styles" applied...
Note how the gray tones are the same? All four maintain the neutral WB but change in their selective rendering of the colors.
Photography is an engineered process based on human vision. The nominal result of the camera design is a "normal" looking image with the default camera settings when two conditions are met by the user:
1) Exposure / Lighting is controlled to record a full range of tone in highlights and shadows SIMULTANEOUSLY:
Outdoor lighting is problematical because scene ranges usually exceed sensor making it impossible to meet the basic requirement of recording detail everywhere. But recording a full range is trivial with studio lighting. Start with a dark room, add fill until shadow detail is recorded then overlap the key light until the highlights are exposed correctly just under clipping ON 3D OBJECTS. Flat charts are not ideal for setting exposure because there are no shadows. What you need for setting exposure is a 3D target like black and white terry cloth. That allows visually seeing when there is detail in the SHADOWS on a black object, and the subtle difference between a clipping highlight that obliterates detail and one 1/3 stop below clipping which retains the see by eye detail.
2) Gray Balance: Gray balance keeps neutrals neutral, no more no less. But it is a very important part of the perception process because we gauge and calibrate our vision to neutrals for tonal range and color. Our eyes adjust to any light not by seeing the teal blue blouse, but by seeing any objects expected to be neutral.
The reason you want to have a portrait subject hold a target for a test shot after setting Custom WB off a gray card of known neutrality is so when looking at the image on the monitor your brain will be able to calibrate to that neutral baseline to more objectively judge the skin tone. Without the target your color perception of the image will be biased by that bright blue clothing.
Capturing with a neutral baseline, and viewing from a neutral baseline are just process control steps necessary to overcome the fallibility of our adaptive color vision. So you open the file with the test target, adjust it with the baseline target in view until the skin tones look "right" then copy the adjustments to the other RAW files without the target.
If you make the adjustments with "styles" it will shift the colors around but retain the neutrals. That's where the Color Checker is valuable. It is easier to objectively see the changes on the chart than in the photo content...
Landscape is a good choice for portraits. Portrait style is actually even worse tending to over saturated the reds. But look at the target. Despite the over the top shift in the colors the perceptually important neutrals on chart and in the clothing have remained neutral. That's how profile based color management works.
Open an image in ACR, then click on the camera icon tab to access the style menu. Abobe, when adding a camera to ACR, creates profile which duplicate the camera styles. Try all with a test image like the one above as see which is the best "fit" for that subject. If one of the pre-sets isn't perfect you can tweek it with the sliders and save it. That selection also then becomes the default for all the other RAW files you open until you change it to something else.
By changing the color via the Styles menu you will be moving the colors around without affecting the overall gray balance as you would by moving the "Temperature" (blue/yellow) and "Tint" (green/magenta) sliders in ACR. Within Photoshop functions like Hue/Saturation and Color Balance will shift color without changing gray balance, but functions like Photo Filters, Color MIxer or adjusting channels separately with Levels and Curves.
There are times when you will want to move everything, including neutrals, warmer or cooler to change the mood of the photo, or adjust Tint to get rid of a green color cast when shooting under trees.
It's important to understand the difference between shifting WB and selective color editing and the MacBeth Color Checker is a tool designed to allow you to see the difference when adjusting color in your images. The goal is making the results look "normal" or not. The chart allows you to quantify the differences visually from knowing what the target usually looks like, and numerically with RGB eyedropper readings.