How do the Mormons define an "Atheist?"

[_haleray]

I don’t consider any one in a religion as an atheist. Buddhists, Taoists, Vedantists, and Confucianists, may have a belief of God that is different than mine, but that doesn’t mean that they are atheists. What I consider as an atheist, is a person that doesn’t believe in any form of God, or chooses NOT to worship, in any form, a God, or religion.

[_Uncle Dale]

I don’t consider any one in a religion as an atheist. Buddhists, Taoists, Vedantists, and Confucianists, may have a belief of God that is different than mine, but that doesn’t mean that they are atheists. What I consider as an atheist, is a person that doesn’t believe in any form of God, or chooses NOT to worship, in any form, a God, or religion.

That's a little closer to my own views -- though some of the religionists
mentioned in the list are technical "atheists."

Perhaps there is a middle ground between religious theism and anti-religious atheism.
If so, that middle ground would provide existential space for non-religious theists,
agnostics, and religious atheists (such as Buddhists).

[religious theism] ------------> [ middle ground ] <----------- [anti-religious atheism]

I suspect that very few of the posters at this MB consider themselves to be
anti-religious atheists -- people who have a testimony that God is a fiction.

UD

[_JohnStuartMill]

...

Mormons don't call Muslims or Zoroastrians atheists. They call them Muslims and Zoroastrians.
...

But Mormons probably DO think of Buddhists, Taoists, Vedantists
and Confucianists as being "atheists."

Sure, because those adherents don't believe in a god or gods.

There is a strain of gnosticism which views all the deities as part
of a vast delusion -- and yet still affirms a shared Divinity at the
core of all human beings.

Like with the extraterrestrials example, I think this comes down to whether the shared Divinity of life is considered to be a god. I suspect most Mormons would say "no".

I am not talking about the sort of pantheism which affirms all the gods,
but rather the recurring philosophy, found in several cultures, that
professes we all are One (One being more than just the sum total of our minds).

So -- what might Mormons call THAT sort of religious person? One who denies not only the plurality of gods, but also the trinity, and God as a celestialized being?

I don't think the plurality of gods or the trinity are atheism litmus tests for Mormons, because they don't think that Jews and Muslims are atheists. I don't know enough of what you mean by "celestialized being" to comment on how important that would be.