Red (vermilion) is a color that makes your field of view feel brighter. Japanese traditional tableware and bowls are often painted with red Urushi, the reason for this is that the red colors accents the contents of the bowl making them look brighter and more appealing. For example in clear soups, if the inside of the bowl is red, it’s also easier to determine each ingredient in the soup.
The Red color seems to also leave less afterimages and decrease reflections from the inside of the Mengane. When doing Kendo and you see your opponent through the Mengane, you rarely even notice that there is actually a Mengane before your eyes. This is also an effect of the red color inside of the Mengane, making the Mengane feel less disturbing when you are wearing your Men.
This knowledge has been passed down by our ancestors who learnt this through experience, and this is still applied when making Bogu even to this day.