Based on the sample images you've provided, AWB appears to be working fine. Neutral objects appear neutral: The plate, the concrete wall, the gravel path, the door, the gray shirt.
You are likely not getting the colors you want because of the color profile on your camera or raw processing software does not match your preferences. Camera and lens selection may also play a role.
Lenses may transmit different frequencies differently. For instance, some produce warmer colors, while others are cooler. Some lenses also have defects, such as "glow", when shot wide open. Some people find that a soft-focus look is pleasant in portraits.
Auto white balance in some cameras normalizes color differences between lenses. In other cameras, it does not. Setting custom white balance typically neutralizes many lens color differences.
If you are disciplined, you should set custom white balance. However, if you shoot in conditions with varied lighting, forgetting to change white balance can result in dozens of subsequent shots being ruined or wasting your time in post processing. (How significant this is depends on your workflow.)
Some cameras allow color-shift adjustments to auto white balance. Since AWB on my camera tends to produce images with more magenta than I'd like, I adjust AWB to increase the complementary color, green.
You should also select the color profile on your camera that best matches your preferences. Usually one or two profiles will subdue magenta-red colors. Available options vary by camera maker:
- FujiFilm: Provia, Velvia, Astia, Classic Chrome, ProNeg-High, ProNeg-Low.
- Canon: Standard, Portrait, Landscape, Neutral, Faithful.
- Nikon: Standard, Neutral, Vivid, Portrait, Landscape, Flat.
- Olympus (Picture Modes): i-Enhance, Vivid, Natural, Muted, Portrait.
Sony (Creative Style): Standard, Vivid, Neutral, Clear, Deep, Light, Portrait, Landscape, Sunset, Night Scene, Autumn leaves.
(Feel free to suggest edits with camera makers and profile names...)
Cameras also typically allow adjustments to saturation, contrast, highlight, shadows, noise reduction, and sharpness.
The objectionable skin tones are most likely magenta, less so red. Even if the colors are accurate, you may still prefer less magenta.
Many tools do the same thing. The concepts underlying curves and levels apply to nearly every other color adjustment tool. Aside from that, use whatever tool is available or that you like best. Regardless of what you choose, it's helpful to know which primary and complementary colors go together (Red-Cyan, Green-Magenta, Blue-Yellow), as well as distinguish Red-Magenta and Blue-Cyan.
You can reduce the magenta by adjusting curves to increase the complementary color, green, in relevant areas. Use color-layer blending to avoid changing the overall luminosity of the image. Use layer masks to isolate changes.
You can do the same thing by adjusting levels. You can use the "auto" button or select white, gray, and black points with the dropper tool. Then look at each channel to see what the software did to use as a starting point for your own adjustments.
Sometimes desaturating slightly is enough to fix skin tones. Use a layer mask to isolate changes.
Some people like HSL/HSV/HSB adjustments. I don't use them at all because I don't know how to adjust "Hue" to get intended results consistently.
You can also try adjusting temperature and tint. (These, along with saturation, are the main color adjustment tools available in Google Photos.)
Some editors include skin-tone specific tools. If these are available to you, experiment with them until you find settings you like.
Here is the result after adjusting the magenta-green curve, masking to limit the effect to the face, desaturating slightly, and applying a contrast mask: