AI will pick whatever Religion that region has in real life. So Polynesia and many others pick Catholicism, China will pick Daoism, Greece will choose Eastern Orthodoxy, so on. Of course only person gets each religion, so after that they just go in alphabetical order (so Buddhism normally goes next). I think Catholicism is the most common religion among the civs, so its the hardest to get. Of course the icon has no relation to what beliefs you take
A cool tip for this, Korea is the only Confucianism, Japan the only Shinto, and China the only Daoism. So if you see that religion chosen but haven't met that player yet, you know who took it!
