I like all the ideas I've seen here. I was originally gonna write up my own thread on how to make Spiritualist empires more interesting, but I did a quick search, and it turns out I'm not the only one who's had complaints.
I always figured it kind of odd that Spiritualist empires just naturally get along, even though, by all accounts, their brands of spirituality should have various points of conflict thanks to the circumstances of how they arose. Human history alone has countless examples of religious wars; hell, Paradox's own Crusader Kings games allude to them right there in the title. Right now, the Spiritualist ethic doesn't really offer much more than extra unity, cheaper edicts, restrictions on AI rights, and flavor.
I believe that, if an empire is invested enough in religion that it's one of their driving ethics, then there should be a state religion that serves as the focal point of life. When you start the game as a Spiritualist empire, nearly all of your pops follow this religion. You get special, separate civics to customize your state religion with; the Exalted Priesthood, Imperial Cult, Death Cult, and Gospel of the Masses civics would all be moved to this separate list, at the very least, while new options could concern things like charity (perhaps a "Social Gospel" civic that functions like a religious version of Shared Burdens), productivity (perhaps a "Work Ethic" or "Good Works" civic that increases worker productivity and happiness), slavery (sanctioned by the divine, or an abomination?), warfare (are we a society of holy warriors, or peacemakers?), relations with other species (are we the divinely chosen superior species, or is our way open to all sentient life?), and the finer details of religious practice (how many gods, what is the afterlife like) -- most of them dependent on whatever other ethic(s) you chose. I'm specifically thinking of the religion system in Civilization as a model here, with its thorough customization of religious tenets.
Spiritualist empires don't even necessarily have to be hostile to AI, either. In real life, animistic faiths imbue inanimate objects with all manner of spiritual meaning; traditional Japanese religion, for instance, believes in tsukumogami, tools that have acquired actual spirits. Even on a secular level, some branches of transhumanism have religious overtones with regards to humans becoming like gods. Materialist empires, too, could have secular reasons to be hostile to AI and automation, ranging from perceived threats to working-class employment to the possibility of losing control and being made obsolete (as the game's Driven Assimilators, Rogue Servitors, and Determined Exterminators demonstrate). It would make perfect logical sense to have a Spiritualist empire that regards robots and AI as expressions of the divine, and synthetic ascension as a path to godhood, as well as a Materialist empire that deeply distrusts AI and keeps it suppressed, seeing it as something that they can't control. (The current Spiritualist fear of robots and Materialist embrace of them, of course, are also options for civics.)
If yours is an evangelistic religion that believes xenos should be saved rather than purged (why?), then you should be able to make efforts to spread your religion to other empires. Commercial pacts and migration treaties will lead to the slow, natural flow of your religion beyond your borders, while more active measures include sponsoring missionary work and, of course, holy war like Paul Atreides from Dune or the Covenant from Halo. Now, of course yours won't be the only religion in the galaxy. Other Spiritualist empires will have their own religions, and some of them may try to convert you. As such, you will also have options to restrict the spread of foreign religions within your empire, ranging from influence campaigns to discourage religious drift among your citizens to a more heavy-handed inquisition.
The reverse is true as well, and if you get too pushy spreading the word of your god or gods within the borders of other Spiritualist empires, then you might suffer a diplomatic penalty. Materialists, too, will also not take kindly to spiritualists trying to proselytize their silly, outdated superstitions, while Xenophobes will see your religion as a Trojan horse for foreign domination. Non-Spiritualist empires without a state religion can take the same measures to limit the spread of foreign religions within their borders, though Xenophobic empires are free to clamp down harder while Xenophilic empires have their hands tied. And if you embrace Spiritualist ethics after the fact, you have the choice of either converting to your empire's largest religion (which will be under the control of that religion's founder, but which will get you a huge diplomatic bonus with them) or founding your own state church spun off from said religion in something of a reformation (which gives you more control but comes with a huge diplomatic penalty, even bigger than for following a separate religion altogether; after all, you're now a heretic).
I especially like the idea of introducing religion as part of a broader rework to culture, which in this game is largely an afterthought in favor of economics, the military, and lately diplomacy. Culture could be used to spread your religion, as it historically has here on Earth. The reverse would be true as well: the cultural strength of a Materialist empire could also dampen enthusiasm for religion, and if your empire is culturally weak, it grows more open to religious (or secularist) conversion by other empires. Xenophilic empires would have a bonus for putting cultural pressure on their neighbors and trade partners, while Xenophobic ones would have a bonus for resisting such. Unity and Amenities output would factor heavily into culture, giving a new purpose to cultural sites and holo-theaters.