Like the social engineering choices in SMAC, the factions can use the any of the Affinities, but some Affinities are more suited to some factions than others. (Some quotes are from the games but most are made on the spot.) Each faction is based on a particular ideology, with the SMAX factions being based on social movements.
UN Peacekeepers: Liberal Democracy
Purity: It is in the past that shows where Humanity is heading in the future. Probably what the faction lean towards due to their preference to Earth culture and following the UN Charter.
Supremacy: Freedom of information is the only safeguard against tyranny. Humanitarian programs would help more if the human mind can be saved from death and disease.
Harmony: We adapted to our planet to heal ourselves. Why not do the same here? Humanitarian programs would excel once humans can live in the planet without the need to potentially faulty suits and incompatible biology.
Human Hive: Communists
Purity: Only those of sufficient Enlightenment can help in guiding Humanity into greatness. Hive philosophy is a mixture of Buddhism, Confucianism, Communism, and Legalism. They would try to promote some Ancient China feel while mixing it with Marx's Communism.
Supremacy: He who controls the input becomes the master of the output. In Hive philosophy, and from the GURPS source book, each individual becomes suited to their proper field of expertise. There are no individuals, only robotic units for the Hive.
Harmony: Expand your awareness into the self of group and into the self of humanity. Like supremacy, each individual will be defined by their position, but more like an ant colony. The workers are genetically made to be the best and the such.
Morgan Industries: Capitalists
Purity: Buy Morgan's new book, Mythology for Profit With emphasis on Old Earth, one can corner the market of Old Earth artifacts and retellings, from movies to books to art, history is a market that can be commodify.
Supremacy: Energy is the currency of the future. Robots have less needs and less maintenance than people anyway.
Harmony: A sustainable ecology is a sustainable economy. Advances in genetics means profits in many markets, from cosmetics to agriculture to healthcare.
Gaia's Stepdaughters: Environmentalists
Purity: We planted on the new planet a sapling of White Pine, to remind us of the mother we left behind. A purity Gaians view more on Earth nature than Earth culture. Pretty much Romanticism in a more New Age angle.
Supremacy: We remove ourselves from nature, to prevent despoiling it with our polluting touch. Basically robotic ecological caretakers.
Harmony: The planet is a living organism and like an organism, we must take care of it and it will take care of us. The Gaians is clearly a harmony faction. Especially with the 'canon' ending of SMAC with them winning through Transcendence.
Spartan Federation: Militants
Purity: Proper training and preparation will make us better than our namesake soon enough. Clearly following the Spartan way of life, including killing unwanted and weak children.
Supremacy: To survive in an alien planet is by making sure it doesn't harm us. They would make themselves into military robots, even in times of peace. Built in guns, laser weapons, advance sensors, the works.
Harmony: We must adapt or we will surly perish. Same with Supremacy but in a more biological way. Gills, wings, genetic enhancements, the works.
Lord's Believers: Religious Fundamentalists
Purity: We must dissent. Clearly a Purity faction, Promise Land and all that.
Supremacy: The serpent shorten our lifespans with the temptation of Eve. Only by transferring the soul to a body the devil can't destroy will we have the first triumph over evil. Hard to image Miriam going all robot but as the spiritual leader, she can justify it through her theology.
Harmony: The Lord God made this world as a new Eden. We must not corrupt this blessed land with our sin. Instead, we must cleanse ourselves and hope God accepts our repentance. Like with Supremacy, it's hard but not impossible to imagine her going in this route.
University of Planet: Technocrats
Purity: Just because it is history, doesn't mean we can't learn from it. One can imagine some Oxford-Cambridge-Ivy League combo the size of a country.
Supremacy: By merging ourselves with computers, our ability to research and learn increases tenfold. Probably what the University followed in 'canon'.
Harmony: The planet is a giant supercomputer. By becoming one with it, we can finally reach optimal research capability, maybe even more. A biological version, with bigger brains and enhanced senses for more accurate research.
Even the human SMAX factions can be Affinity compatible as well, with some factions leaning more to one faction than the other.
Data Angels: Minarchist Libertarians
Purity: The old Internet was the center of freedom and individuality. Being the hacker faction that promotes individual rights, they would probably be the next Anonymous and open source movement.
Supremacy: Which one is important, the data or the jazz? This is probably the leaning affinity for these guys, if it weren't for the fact that they're against invasive anything.
Harmony: To be free, one must also be free to choose what they look like. Being individualists, being able to change your genetics by choice makes them more diverse and individualistic.
Free Drones: Social Democrats
Purity: It is in the happiness of the workers that we strive for. Clearly a purity faction. It's the attempt to be a communistic haven where everyone gets what they need and what they require.
Supremacy: Better industry makes better products for us to use. Since they're against 'Pie in the Sky' research, it's hard to imagine them going robots.
Harmony: Better agriculture and healthcare makes hunger and sickness disappear from even the poorest among us. Same with Supremacy, it's hard to imagine them going half alien native.
Nautilus Pirates: Anarchists
Purity: We follow the ideals of the ancient pirates, drink, pillage, and raid. Basically a sci-fi version of Pirates of the Caribbean.
Supremacy: If becoming mechs means losing every weakness in the water, why stay human? Robot pirates, soon, robot space pirates.
Harmony: We are people of the sea. To better suit ourselves in it means that we will gain power that those landlovers don't have. Half-fish people pirates.
Cybernetic Consciousness: Utilitarians
Purity: It is only logical for us to return to our roots, for those who do not know where they came from does not know where they are heading. They probably follow an optimized past/history or something.
Supremacy: By removing Right Brain Functioning, our Left Brain Functioning increase tenfold. Clearly the faction's affinity.
Harmony: By improving our bodies, we decrease potential suffering while increasing potential happiness. It's logical for them to improve their biological bodies while bonding with organic based AIs. The planet is a supercomputer after all. This is just simple adaption.
Cult of Planet: Transhumanists and Voluntary Extinctionists
Purity: His Holiness Cha Dawn was discovered by our people growing in an alien hive with the drones bowing before Him in reverence. Again, it's hard to imagine them to go Purity but it would clearly be a promotion of ancient religions and myths of some sort.
Supremacy: Lessen the harm made to planet by transferring oneself into bodies of metal and glass. Eco-robo cult perhaps?
Harmony: I am Cha Dawn, the Voice of Planet. Obviously the choice affinity for them.
