Clerics shouldn’t just be healing anyone, or if they do, they should be extracting a pound of flesh, karmically speaking, from those whose beliefs or alignment are significantly different.
Let’s say, for example, that in the campaign, the gods are completely real and they are at odds with one another or with similarly powerful demons or devils. Why would a priest of Zeus heal a prominent follower of Hades without extracting a price? Do the gods send the energy to the cleric at the time of healing? Or do they give it to them to do as they see fit and then decide whether to keep sending those energies during the night’s meditations?
There may be a few gods in your world that believe in healing everyone, or the possibility of redemption at any moment, even the last. But for the most part, I think there are some interesting situations or house rules that could come up when a priest needs to heal or especially resurrect a non-believer, heretic, heathen or enemy.
Here are some options that come to mind:
The simplest, of course, is to not care when it comes to healing within the party. I like this because the last thing you want is the cleric lording it over the others, “Ahamite the Smug does not regrow the sword arms of those who have not donated a million gold talents to him, payable to his loyal servant, Brother Dick.” But when NPC’s are healing, it’s entirely appropriate and a good plot hook to set a price, be it gold, a quest or some specific vow or service. At the least, the patient should vow to never desecrate or blaspheme the god who is providing the help.
Or you could allow the cleric to exact certain demands, pre-approved by the DM, when the first opportunity to heal arises and have that apply throughout the adventure.
Another way to do this would be to keep tally of every ten HP healed by any god’s cleric and translate that into a karmic debt to the god specifically, with whom the patient must bargain at some later date. Ten HP might mean a week of service or contemplation. Fifty points might mean a major favor, such as escorting a monk or protecting a valuable relic. A hundred HP? Consider conversion! Or at the least, the PC should become intimately familiar with the faith and speak openly about how much she admires the wisdom of the Aardvark god.
The further apart the two faiths are, the more likely some sort of conflict or even alignment change will come into play.
When two clerics of different faiths are involved, one as healer and one as patient, it might be up to the players and DM to decide whether the healing would be given, whether it would work and what sort of effect it might have on the relationship between both clerics and their gods.
Whatever you decide, the consequences of breaking an oath or quest or a betrayal of that god should immediately result in the loss of all HP ever healed, limb regrown or perhaps even life given. It might also include some time in the afterlife of that god, atoning.
It can be as complicated and difficult as you decide it to be as long as it is interesting and adds something to the game. Obviously there is a lot of potential to add not-fun to the game. But clearly, if you were talking about a polytheistic fantasy world with gods of various alignments, this sort of thing would naturally come up.
The last way is, of course, to make no definite statement on whether the gods exist, and decide that the spells work because the gods see things we cannot (or it just works because there is no Loki vs. Thor, just two cults taking power from the plane of energy).
I’d love to hear your ideas, by the way.