Turn Undead as a Skill: This seems like a pretty obvious thing to me:
• Faith (Charisma) is a class skill for any class that gets or advances Turn Undead.
• You can use Faith in place of Heal when dealing with other believers. Faith is treated as magic for the purposes of stuff like healing Mummy Rot.
• You can use Faith in place of Intimidate; using Faith ignores the immunity to Fear due to type. However, you can only use Faith to demoralize against enemies of your deity (undead for Pelor, for example), and you can only use Faith to adjust someone's attitude if they are also a follower of your deity.
• Divine Feats, Domain Feats, and other things that require that you spend Turn Undead uses instead require a DC 10 + (5 * Uses Needed) Faith check.
• Use the table of modifiers for Bluff; however, rather than being based off of how unbelievable your lie is, it's instead based off of how much your deity approves of what you're doing. In other words, your staunch faith helps you more when you're on a mission from god rather than when you're on the way to the corner store.
• Anything that would require the Atonement spell to remove or resolve can be dealt with through a DC 20 Faith check. The recipient still needs to be sincere about the whole thing, and the above modifiers do apply.
• You can "fall from grace" - if you do something really offensive to your deity (like killing one of their Clerics or doing the exact opposite of their teachings), you can't use Faith until you atone.
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Under this shift, a couple changes become obvious:
• Any Domain or class feature that lets you Turn something now just expands what you can use Faith to intimidate. For example, the Fire domain would let you demoralize [Water] creatures and adjust the attitude of [Fire] creatures, regardless of whether or not such creatures follow your deity.
• Nightsticks? Out the window.
• Replace Turn/Rebuke Undead with Skill Focus (Faith) as a bonus feat; use Skill Focus (Faith) as a replacement for stuff that required Turn/Rebuke Undead.
• Stuff that gives you Greater Turning instead gives you Skill Mastery (Faith) - in other words, the Sun Domain will let you take 10 with Faith checks, as would the Deathless Domain.
• You could totally replace Smite Evil with (essentially) the ability to use Faith in place of Iaijutsu Focus... but only against stuff it would normally let you Smite (rather than Flat-Footed creatures, and forgoing the need to have just drawn the weapon.)
• Similarly, I could see Divine Health being replaced with the ability to use Faith in place of Autohypnosis. Maybe restrict the memorize function to memorizing scripture and prayer, and let you treat diseases as poisons for the purposes of Tolerate Poison?
Heck, there might be a Paladin fix in here somewhere.