I have just been looking at this. The two colours are traditionally linked in Celtic lore (with black as the third).
For example in the Merlin stories he prophesies two dragons are the cause of a continually collapsing tower. The two dragons are Red (representing the British) and one White (representing the Saxons). Also the two springs at Glastonbury, the Chalice Well (red water) and the nearby Whitespring.
The two colours are usually assigned Red as Feminine (representing menstral blood) and White as Masculine (representing semen). With Black they represent the Triple Goddess (think Snow White - skin like snow, hair like ebony and lips like blood). Together they also link to the Fly Agaric (Amanita muscaria) mushroom, which is known for its hallucinogenic properties.
Throughout the Greenwood there are red and white dots, always together. In fact Red and White are paired in a significant way on fifteen cards.
The polarity of the major cards is as follows:
Red: Archer, Justice, Blasted Oak, Strength, Death, Guardian.
White: Pole Star, Ancestor, Lovers, Balance, Reflection, Wheel of Fortune.
Neither: Fool, Greenwoman, Greenman, Hermit, Judgement, Seer, Shaman, Moon, Sun, World Tree.
Placed on the Wheel of the Year:
Imbolc: White - Ancestor, Pole Star
Spring Equinox: Red - Archer, Justice
Beltane: White - Lovers, Balance
Midsummer: Neither - Greenman, Greenwoman
Lammas: Red - Blasted Oak, Strength
Autumn Equinox: White - Reflection, Wheel of Fortune
Samhain: Red - Death, Guardian
Midwinter: Neither - Hermit, Justice
So the opposing festivals are the opposing colours:
Imbolc white - Lammas - red
Spring Equinox red - Autumn Equinox white
Beltane white - Samhain red
Midsummer neither - Midwinter - neither
What all of this means exactly, I'm honestly not sure. I can see the edges of it, but I haven't quite reached full understanding. I'll come back when my ideas are more fully formed.
FS
Edit to Add: I missed these the first time through, but I just found these in the companion book:
The Lovers said:
A handfasted, foliate man and woman stand side by side creating a polaric interchange that generates a Maypole, here symbolized as a living birch tree. Spiralling around the birch tree are green garlands, reaching toward the sky and representing the ascending earth energies (red) meeting the descending air/sky energies (white).
Balance said:
The red and white energies represent the basic colours of a primal world - blood, fire and iron are red; milk, ash and bone are white.
Even if you don't have a full understanding, the way you laid things out and explained them help me understand this a lot better!