@Kordishal Here is how I imagine religion being implemented in Stellaris.
Religion essentially gives your POPs an additional trait. These bonuses are minor and one-dimensional e.g. army damage, energy credits, growth, etc. You get to name your own religion.
There are policies that determine your governments attitude towards religion.
- "State Religion" means what it implies.
- "Tolerant" means other religions are second-class citizens.
- "Secularism" is what it implies. No state religion, but very weak religious bonuses.
The strength of the bonus granted by religion scales with a few things. These include your empires policy towards the religion, whether the POP is spiritual, and the happiness of the POP.
POPs with a different religion than the state religion will be unhappy if they live in a sector with a governor who belongs to a different religion.
Other empires will be unhappy with you if have POPs with their religion in your empire and you persecute them ("State Religion," or "Tolerant."). Or if you have a different religion than them and they are fanatic Spiritualists.
Materialist and Individualist locks off the "State Religion" policy. Spiritualist and Collectivist locks off "Secularism." And Fanatic Collectivist locks everything except State Religion.
There is a "neutral" religious trait called "agnostic" which gives its own bonus (probably -Xenophobia). This is the trait for anyone who doesn't want a religion. And yes, you can be "agnostic" and Fanatic Collectivist, but a Fanatic Collectivist will impose agnosticism on the entire population.