This is first time I've played a cleric in decades. To be honest, I really don't mind playing support character and letting other people "get all the glory." It's a new thing to me. Just don't steal my s##t!!
See, the thing is I don't really see actually following what your character's deity would be likely to wish (few gods would look kindly upon the desecration of corpses put to rest with proper burial rites), as escalating the situation. Certainly not if other characters are using their alignment as an excuse for their actions, even when the DM essentially backs your character up, and mentions that the body appears to be sanctified with a burial rite. And me? I would probably punctuate their protestations as other stabilize them once they awaken that they are lucky all that happened was a member of the faith didn't heal their wounds, for many who anger the gods, especially the gods of the dead, suffer far worse fates.
The thing about being the party healer is you should not, in fact, be obligated to heal everyone, all the time, unless it is specifically the tenet of your deity. And there are a very small number of deities who are neutral gods of healing, who insist that you heal ALL in need. And those kinds of characters, well, they bring a whole other bag of awesome tension to a group. Because the BBEG? Who was mortally wounded but not killed by the group? A cleric of that sort of god of healing HAS to heal said BBEG immediately. Doesn't matter if he was just found murdering a thousand children. About the only time such a priest doesn't have to heal someone is when they're undead. At which point they happily heal that undead, because it hurts and eventually destroys them.
But no, really. If something sounds horrifyingly distasteful to most people, it's probably not a thing that should be done. And the second that body was shown by the DM to be someone properly sanctified and buried, then MOST people would be REALLY upset if something were to happen to such a body. It's the exact same as exhuming their corpse from the ground and stealing what's on them. It's effectively graverobbing, and most societies punish that very severely indeed.
Honestly? It's a roleplaying teaching moment: Chaotic neutral, or whatever other alignment, is not a get out of jail free card for doing things that society would normally punish you for. And your party members, people traveling with you? If it's in character for them to be aghast at such an action, then it's appropriate for them to respond accordingly. And that might very well mean you're on your own for committing an atrocity. It's like if the party is going around town, and a rogue PC gets tossed in jail because they get caught breaking and entering, or otherwise stealing. Maybe...just maybe...they should think about their actions before they take them, and not use an alignment as a validation for bad behavior.