Depends on
1. Civs being played (And cultural history)
2. Numerical orders of founding (This associated to specific Holy District Buildings associated with a religion. Wat, Cathedral and Meeting Houses are preferred AI regardless of what religion they chose, but they choose real life ones and Custom 'Zodiac Religions' were left to players)
Personal choices.
Catholicism if
1. The AI hasn't picked the religion YET.
2. The Following Civs are being played: Spain, France, Rome, Brazil, Poland
3. Cathedral (or Meeting house) is still available
Protestantism if
1. The AI hasn't picked the religion YET.
2. The Following Civs are being played: America, England, Norway, Germany, Creeks.
3. Meeting House (or Cathedral) is still available
Eastern Orthodoxy if
1. The AI hasn't picked the religion YET.
2. The Following Civs are being played: Greece, Macedonia, Russia, Mongolia (They were a kind of Christian before, actually they were a kinda heretics by major churches standards, eventually they converted to the religions practiced by conquered peoples as well, particularly in the Caucasus and India)
3. Either Cathedral or Synagogue are still available
Anglicanism (Leo zodiac symbol) if
1. England or America
2. AI Already picked Protestantism
3. Holy Site buildings of choice: Pagoda, Meeting House, Cathedral, Synagogue or Dar el Mehr.
Judaism if
1. Catholicism, Protestantism or Eastern Orthodoxy are all taken
2. The Following Civs are being played: America, Spain (See Item 1), Egypt, Scythia, Russia (Again, See Item 1)
3. Synagogue still available
Buddhism if
1. The AI hasn't picked the religion YET.
2. The Following Civs are being played: Japan, Khmer, China, (and maybe others)
3. Either Wat, Stupa, or Pagoda still available. (AI doesn't like Stupa much)
Hinduism if
1. The AI hasn't picked the religion YET. OR Buddhism is taken first
2. The Following Civs are being played: India, Indonesia, Khmer (They were Hindus before they became Buddhist), and maybe others
3. Either Wat, Stupa, or Gurudwara are still available. (AI doesn't like Stupa much)
Confucianism if
1. The Following Civs are being played: China, Korea, Japan, Greece, Rome, Macedonia
2. Confucius is awarded or purchased.
3. Either Pagoda or Wat are available (Pagoda is not AI favorite ones)
Taoism if
1. The Following Civs are being played: China, Korea, Japan,
2. Laozi is is awarded or purchased.
3. Pagoda is still available (Pagoda is not AI favorite ones)
Stoicism (Either Lion or Libra zodiac sign is chosen) if.
1. Prophets earned aren't big names (Particularly Christian Saints)
2. The Following Civs are being played: Greece, Rome, Macedon.
3. Wat, Cathedral or Meeting House are taken by AI.
Brotherhood of Nod (Scorpio zodiac symbol) if
1. Prophets earned aren't big names
2. Plays as either Egypt or Nubia
3. Wat, Cathedral or Meeting House are taken by AI.