If a friend is dying, and then isn't dying, we'd generally say that they were healed, even if they didn't regain consciousness, so I'd absolutely say my take is within the spirit and scope of the OP. That said, I'm not personally against actually restoration of hitpoints or conditions, either, but the cost/risk would likely go up.That doesn't seem an accurate summary.
The OP posits a fighter simply praying to the gods for healing with a dying friend and asks how a DM would handle it. Not specifically for stabilization, which the fighter can do with the explicit mechanic of a medicine check. Divine intervention healing is not limited to stabilization. The 2e FR god books have examples of big time divine intervention healing. An answered prayer for healing could be stabilization but could be a lot more.
If you are going for a religion check to stabilize though there seem more relevant mechanics to compare it to than cantrips or healing kits. The relevant comparison of a not explicit use of a religion check for stabilization seems to be the explicit mechanic of the medicine check for stabilization.
What skill checks do you expect a religion check to be able to substitute for? You can pray in a lot of situations.
I mention the healer's kit because it's something available to everyone (thus no niche protection) that autosucceeds at stabilizing a dying friend. Thus, I find it relevant as a reference point for how you can do the thing without having to ask the GM to allow it. I'm not even sold on religion being necessarily relevant -- I'd easily allow a CHA(persuasion) check for praying for aid. Religion is also on the table. Need to see how the player proposes to go about it and how the negotiation resolves.