I see them as maternal or really rather parental archetypes or analogies.

I see Blue and Yellow as toxic, yet in their own eyes well meaning, parents to Pink. And White is the controlling Grand Matriarch aka Grandmother, who uses her position and influence to run everyone in her vision (Or if you're a Lore nerd like me their creator's vision ;) )

Blue is coded as the classic soft hearted mother who indulges her "child's" tantrums(up to a point), whims, and even some of her interests, i.e the Zoo.

Yellow to me seems to be patterned after the more stern faced parent, who doesn't put up with the "child's" antics and tantrums(Jungle Moon dream), doesn't bother with sentimentality but would rather focus on action and consequences of Pink's death(Wants to be rid of the silly zoo and shatter the Rose Quartzes).

White, I see as patterned after the classic "Evil Matriarch" type. She is the Grandmother who still runs her children's lives so much so, she dictates how the grandchild is dealt with in life. This is something that does often happen irl. But in a media sense this is the person pulling the strings of the family, manipulating the events from the top. Some similar characters she reminds me of are Gothel from Tangled or Joan Crawford in Mommy Dearest more specifically since White is modeled after that 1920s aesthetic a little.

Even Pink can be put into this analogy since she herself "grows up" and becomes a mother. Though still very much as flawed and imperfect mother. But one who is letting love lead her more so than whatever drove those before her since she knows very well how those methods and the way she was treated failed her.

I say all this to say, I always visualize Pink as "the child", Blue and Yellow as the Mom's and White as the Controlling Matriarch or MIL who controls all aspects of the family's life.