Milk is white and everything white is racist, so, no.....................
There are various origin myths about the “river” of stars in the sky known as the Milky Way but the most well known and why it is called that is the Greek one...
From wiki
The Greek name for the Milky Way (Γαλαξίας Galaxias) is derived from the Greek word for milk (γάλα, gala). One legend explains how the Milky Way was created by Heracles (Roman Hercules) when he was a baby.[15] His father, Zeus, was fond of his son, who was born of the mortal woman Alcmene. He decided to let the infant Heracles suckle on his divine wife Hera’s milk when she was asleep, an act which would endow the baby with godlike qualities. When Hera woke and realized that she was breastfeeding an unknown infant, she pushed him away and the spurting milk became the Milky Way.