The historian Yuval Harari writes about the various types of religions that have existed over the millennia. He points out that in the modern period, ideologies (e.g. nationalism, liberalism, socialism, fascism) play more or less the same roles that religions played in the ancient period, complete with central teachings, prophets, holy texts, heresies, holy wars, and so forth. The modern ideologies all fall within the umbrella of humanism, which worships humans instead of gods.
I'm not sure how on-board I am with Harari's interpretation, but if I were programming a Civilization game from scratch, I would probably use the same mechanism for religions, cultures, and ideologies.
At any rate, here are some that could be added.
- Unitarianism. Unitarianism already exists, of course, but it seems like the kind of thing that could grow in an increasingly globalized culture. It might also be a reaction against high levels of religious extremism that are prevalent today.
- Some science fiction authors portray fictional religions which revolve around the belief that the world is a simulated reality. A person's objective is to awaken to the true reality. I can imagine several factors converging to cause such beliefs to become mainstream in the future. If physics continues to fail to explain fundamental questions of the universe, if people become uncomfortable with increasingly invasive technology, and if the world economy stagnates, then result is that the public may lose confidence in science-based answers and look to new sources.
- Transhumanism itself, if not a religion, at least has many of the trappings of religion.