The red team members were those trolls who have dream selves on Prospit, and the blue team were those whose dream selves are on Derse, with the exception of Sollux, who has two dream selves, one for each of the two kingdoms. This is a clear reference to his duality theme, as the Gemini troll, but perhaps also would allow him, as the one who set the teams up, to "watch" both sides.
Notably, the leader of each team has the same blood color as their team color.