Religion is linked to culture and ethics in the game. One can assume that religion pays a big role in cultural conversion of civilizations and in the civilizations ethical code.
Developing the seperate distinct nature of your civilizations dominant religions would be part of the culture tech, while developing the core principles of your dominant religions would be part of the ethical techs.
Adding religion as a seperate aspect of the game, is well an interesting idea, as at present all religions are really unsuited to alien life forms and I think there would be a huge theological schism between those who believe gods message is meant for humans and god has his own plans with the aliens and those who believe they have a destiny to convert aliens too to the true faith. The first religious tech would be xeno-conversion, that is the adaption of the religion to aliens, which would increase your ability to convert worlds of other religions. Basically if you share a religion+an ethical alignment you get even greater relations bonus, while if you have a different religion+an ethical alignment world under your influence, it is easier to convert if their civilization is of a different religion to the world and that world is of your civilization's religion.
I can think of the following 8 basic general religions for all civilizations, human and alien.
Monotheism- Belief in one god which is held to have made the universe.
Dualtheism- Belief in the universe as the result of two gods, one of which created each thing and the other it's opposite.
Poliytheism- Belief in multiple gods, holding power over different aspects of the universe.
Philosophical- Belief in transcendant philosophical concepts as goals for life, without much emphasis on divinity.
Athiesm- A lack of belief in gods or transcendant philosophical concepts.
Precursor worship- A belief in the divine nature of the precursers.
Agnosticism- A lack of strong belief for or against any particular religious concept.
Magical- A belief in wielding and/or contacting with supernatural forces and entities, to chosen ends.
Each of these would have 5 opposed techs, to be researched and representing the religions development either away from it's original roots or towards them and a final 6th unified religious tech, which requires an advanced research tree tech, close to the tech victory to research and an original tech based on converting aliens.
My proposal for the religious techs for monotheism would be thus
Xeno-conversion (requires universal translator)- Before now, our religion was essentially focused exclusively on the texts handed down to us by our ancesters and even as we made contact with alien life forms, we did not presume to share those texts with them. With the help of the universal translator, we have translated those texts, not merely in word but also in meaning so that aliens can understand them.
Allows us to send missionaries to alien worlds.
Now there would be the five forms of research, one of them would be religious universalism while the other would be religious exclusivism.
Religious universalism-
1. Universal divine plan- We have realised, due to our religious exchanges with other civilizations, that other species have been endowed by god with more or less the same religious understanding and each has their unique part in the divine plan. When god made them all, he understood that they immediately needed different texts and the time has come to apprecitate this.
Diplomacy when dealing with other monotheist civilizations +5
2. Basic religious synthesis- Our understanding of the divine plan, has began to coalesce with that of the other aliens who believe in one god, at least in the fundermental respects
Diplomacy when dealing with other monotheist civilizations +5
Religious conversion effectiveness- +5%
3. Advanced religious synthesis- We now have developed a common theology with those aliens who believe in one god which is understood by the aliens.
Diplomacy when dealing with other monotheist civilizations +5
Religious conversion effectiveness- +5%
Cultural influence- -5%
4. Universal revelations- New prophets have begun to recieve revalations which are relavant to all species, without any need for a great deal of translation. We now see that god's plan is adressed to the entire galaxy, to an even greater extent.
Diplomacy when dealing with other monotheist civilizations +5
Religious conversion effectiveness- +10%
Cultural influence -10%
5. Common Faith- We now have a common faith, absorbing the worthwhile elements of all alien civilizations. The dream of religious unity is close at hand.
Religious conversion effectiveness- +10%
Influence- -10%
Religious paternalism-
1. Religious elitism- We have realised due to the contact of our brave missionaries with the aliens, that alien religions are hopelessly corrupt and misguided in their religious beliefs. We alone were given the true divine plan, although it is our duty to share it with the aliens as long as they renounce their false beliefs, our species has a unique relationship with the divine.
Conversion resistance- +5%
Influence- +5%
Diplomacy -5%
2. Religious obsuritanism- Our texts have been refined to the point that, it is more or less impossible for any unenlightened alien to understand it, except with one our species to interpret it. By this way we can ensure foul xeno-heresies do not creep into our religion.
Conversion resistance- +5%
Influence- +5%
Diplomacy -5%
3. Strict religious dogma- We have begun to identify and categorise our dogmas in the finest detail to the point that it should be near impossible for xeno-heresies to creep in without detections.
Conversion resistance- +5%
Influence +10%
Diplomacy -5%
4. Religious purity- We have finally purified our religion of heresy, whether alien or not. We can now be certain in our faith that we possess the only true divine revelation and those who doubt this will be silenced.
Conversion resistance- +10%
Diplomacy- -10%
5. Manifest destiny- We have a devine mandate, to preach to all other species the truth and this goes in hand in hand with the power of humanity. Those who oppose the will of humanity, defy god's will.
Influence +10%
Diplomacy -10%
Conversion resistance- +5%
The Final tech
Divine understanding- As our species unlocks the last secrets of the universe, we now know the full extent of god's power and the full extent of his transcendance. Our existing theology, fits we believe quite well into the picture. Science and theology are now in complete harmony as the two have finally merged into one.
Research- +10%
Influence- +10%
Religious conversion- +10%
Conversion resistance- -10%
Diplomacy- +10
The basic system is each tech is not compatable with it's opposite number, although you can combine techs of different levels together. So you can have basic synthesis with religious elitism, but not religious elitist and universal divine plan.