Now that we're not burning or crushing people for disavowing the state church we don't need to define the belief system solely on that criteria anymore.

Suppose you firmly believed the answer to the simulation argument was that we are indeed living in a simulation. Who runs the code? By any reasonable definition of god you have some; they may be petty, or foreign, or unknowable but you've got gods all the same. Yes they are not Christian gods, so in that sense the person is still a-Christian-theist but does that still have meaning.

Or suppose the earth was seeded with amino acids by a traveling and functionally immortal alien race who monitor earth by ansible and adjust things for the better every now and again when people ask them too. Athiest? Well sort of.

The claim that there are no simulation masters, no alien races, no omniscient AI spy satellites, no ... is certainly possible, but it seems like we're back to thinking that we humans are special and the center of the universe.

This is partly just a matter of verbal semantics but I think just deciding to be not Christian/Muslim/Jewish/etc. often leads to theological laziness about other possibilities, and as atheism becomes more commonplace (it's hard to imagine that it won't) maybe it won't be enough to just join the camp and call it good.