Four Religions that fully impact the world and the way people react towards you. These Include: The Seven Faced God. The Lord of Light (R'hllor). The Drowned Gods. The Gods of the Old.
Your character's religion can be changed by talking to the man of faith for the respective religion.
If your character and the fief you own have different primary religion, they will slowly disapprove of you.
The Seven Faced God
The Seven Faced God is the primary religion of Westeros.
The Lord of Light (R'hllor)
Essos region worships R'hllor
The Drowned Gods
The drowned gods religion is found in iron islands faction area.
The Gods of the Old
The old gods religion is primarily located in the North and north of the wall.
Other religions such as Mother Rhoyne and numerous minor regions are not included in AWoIaF.