Well, if I were playing either "religious type" in that situation it would absolutely have made a huge difference, and I'm at a loss to account for why you can't see how, so it's obviously a matter of outlook/point of view.
If no GM judgement is present, I am exploring my character's morality from the inside - immersively - at least if I want to. If it's all, ultimately, up to GM decision then the only thing I can explore is the GM's view of what my character's code actually is. I'm sat there, as a player, wondering what the GM thinks, rather than exploring "what my character thinks" in the imaginary world.
The character isn't being affected in the slightest, here - it's the player who is being chucked out. That is all the difference in the world.
Deities are tangible things, sure - but "alignment" isn't - at least, not in any game I've ever played. The concept of that is so flawed that I can't see it ever working; the (real world) controversy over who or what might be said to be a "moral authority" tells me this. It's not that philosophers can't agree on who might be a moral authority, it's that they can't agree on what the term should mean!
Example: earlier on, you said that the GM decides what LG is. Does that mean that, if the GM decides that it's "Lawful Good" to burn down orphanages and slaughter innocents, then that's what "Lawful Good" is? That's one long, slippery slope...