Religions should be started without human or AI intervention as a function of the civilization's total Faith output, Science output, GPT, Culture output, number of religious buildings, existing religions in the empire, existing religions in the world, and a random factor. There should be no limit on the number of foundable religions in one game. When religions are founded, their beliefs should arise based on the circumstances of the holy city (ie a production-based city will have a production-flavored belief set)
Existing beliefs should be buffed and new ones added. Great Prophets should arise spontaneously.
However, religions should also have an added level of strategic depth by not only giving useful bonuses, but by fostering extremism as well; some beliefs, such as Literal Creationism, should grant an x% science penalty and a 2x% faith boost for each follower, but should have a chance each turn of spawning Barbarian units with a +100% boost against cities, a +100000% boost vs. nuclear weapons, and a -10% science modifier in a city for every Barbarian unit with that promotion in the city's radius. An Interfaith Cooperation wonder (Globalization?) should reduce the risk of religious barbarian unit spawning by 50% and gradually cause beliefs such as Literal Creationism to disappear from the map.
Missionaries and Inquisitors should arise at random but should also be buildable to boost desirable religions and harm undesirable religions. A Religious Tolerance SP should give +5%

to

for every belief in a given city, +10%

to

for every separate denomination in a city, and +15%

to

for every religion being practiced in a given city. It may seem OP, but given that this is Community Call to Power it seems the only way to make religion a force to be reckoned with in the late game.
Denominations should arise when two different religions share at least 80% of the same beliefs. However, these will have different religious buildings than the "mainline" religion. Religious buildings should be different between different religions and should not only contribute to the common pool of Faith but generate specific bonuses for the spread of a particular religion. Religious buildings should arise randomly based on how powerful a religion is in a given city, but you may always build buildings of any religion desired artificially in order to enhance a favored state religion. Some religious buildings should enable Missionaries and Inquisitors to be built, but they should be built with Production rather than Faith.
In addition, a new tile improvement, the Monastery, should be available at Priesthood. It should give +3

and +1

, buffed to +5

and +2

at Theology and again to +10

, +5

, and +3

at Televangelism. The Holy Site should give +10

, +2

and +2

, buffed to +20 :c5faith, +5

and +5

at Theology, and +50

, +10

, and +10

at Televangelism. However, Great Prophets will not spawn at a rate directly under the control of the player, and should spawn more rarely in any case, making them even more valuable. Faith should not be usable to spawn non-prophet GPs unless a religion in a city has a belief called Divine Inspiration, which gives GPs as a function of both the

produced by the city and its local circumstances.
A player may also use social policies and units to promote specific beliefs in different cities of his empire and others.
This will create a religion system with a much greater depth and power than has ever been present in Civilization.
EDIT: As Great Prophet appearance and movement will be random, the creation of Holy Sites should NOT take up a tile improvement allocation, merely be a tile improvement (it's possible). Great Prophets should only be necessary to found a new religion or create a Holy Site, not to add beliefs onto an existing religion.