After much research into hair and material settings, I found that this hair glow is directly related to the Specular parameter in the material. In my case, the glow was visible if I set the values for Sky Light Intensity >1 or used Exposure Compensation in the post-process >1. Forcibly disabling Specular from the main hair material and setting the value to 0 makes the hair completely non-shiny and solves the problem. Fine-tuning the Specular parameters helps to achieve better results in different lighting conditions and eliminates the problem of glowing hair.