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Would a cleric lose any advantages, or perhaps spell casting abilites, if he were battling inside the temple of an opposing god? One would imagine that the temple would be warded and built so that every advantage came to their own defense.
That is really a vague question. There is no intrinsic advantage, but it's highly likely that the other cleric will have some defensive spells put up, affecting primarily his enemies (e.g. an unhallow, forbiddance, etc.).
The Book of Vile Darkness has some stuff about the taint of evil on an area. Effects are dependant upon the strength of the taint. There would need to be some really bad stuff going on for a long time in the temple for it to affect anything.