Most standard 3.5e/Pathfinder classes exist unchanged in this environment. Barbarians, Bards, Druids, Fighters, Rangers, Rogues, Sorcerers, and Wizards all exist relatively unchanged. There is no known training for Monks in the current Known World, although rare training for Psychic Warriors is available and shares many similarities to Monk training, and there are stories of a hobgoblin group carrying aspects of the old monk traditions.
Paladins must belong to one of the Holy Militants, and Clerics all must subscribe to Alexandrian Orthodoxy, and be ordained by an accepted episcopacy, either regional or manifest. The vastness of the church further allows specialist cleric styles to grow, such as the Arcane Disciple, the Crusader Cleric, and the Evangelist. Further, while Favored Souls (Oracles in Pathfinder) are rare on the Mainland, they are the primary divine casters in Petera and the Ulan.
The entrenched social structure and relative political stability of this world allow for a new base class, the Professional, to flourish. Perceptive and skilled, this is a variant of the rogue class focuses on leadership and expertise, though has a small number of rogue defensive mechanics.
Also, while it is true that sometimes members of various cults and Alexandrian Heresies have clerical abilities, they are understood to be due to remnants of the Outsider Lord power, and treated accordingly. As such, they are unsuited to player characters.