In most settings divine magic is interchangeable. It doesn’t matter which god provides the positive energy for turning or healing as it all works the same. But why would a god heal a non-believer? I have a few ideas on how healing potions may affect consumers who do not worship the god whose cleric made it. This could be easily applied to healing spells, but I prefer to concentrate on treasure that may (usually?) have some side effects. In most cases, the recipient still heals as normal. There is no save in all cases- drinking the potion is considered willingness to submit to the magic. It is the capricious nature of the divine that results in:

The consumer’s appearance changes. It may be to the god’s preferred race, a tattoo of the god’s symbol on the brow or glowing eyes (the color is god or pantheon specific). Other than bonuses or penalties to encounter checks, this causes no mechanical changes. It usually lasts for hours or days.

The consumer is charmed/geased to serve the god’s mortal servants for a time. This usually lasts for a few weeks or months.

The consumer is cursed. This is never lethal or even serious. It lasts for a few hours or ends with conversion to the god’s worship, which is the point of the curse.

The consumer gains a “friend”, a familiar level critter that tries to convert the character and all those it encounters. Killing it is bad as the consumer takes triple the amount of damage the potion healed. The critter sticks around until it is obvious the character will not convert or does so.

The consumer gains a series of dreams/visions of afterlifes, those of their own god with a negative taint and those of the potion’s god with a positive slant. One merges into the other over a week or so or ends with conversion. The visions occur at times important to the god and may happen at a bad time for the character.

The consumer gains a cleric level. If they use any clerical power and do not convert, they will be getting a visit from an angel (or demon, devil, salad, modron, etc.) who will not be nice. The level does not count against the character’s total levels, experience points or even alignment. At least until it is used and then it becomes permanent. This can really screw with clerics who drink potions made with the magic of gods not their own, not to mention that all of these options are bad news for paladins.