Calling Someone A Non Muslim
What would be an objective reason for you to call anyone anything that they themselves don’t wish to be called?
As I stated above, we need to be clear in the objective. There’s no person who denies God but calls himself a Muslim, so this case is irrelevant. Also all Muslim countries presently are nation states so this kind of distinction is unnecessary in the cabinet scenario too.
Objective is needed to understand the purpose of distinction. For example, a state might give certain rights to either category of Muslims and Non-Muslims. Or a private financial grant might be specific for a certain denomination.
Sure, that could be a valid objective reason. However, in a nation state if they build a mosque, they would have to do the same for people of other religions in that nation too. However, that’s a separate topic.