...who can't define a deity?

Ignosticism sometimes want you to also define what "to believe" means.

Why? You can see in the comment you replied to.

When you are ignostic it is interesting that you can also be, agnostic and Christian by some definitions and antitheist by other definitions... A schrodinger christian.

Seems like it’s gathered quite a wide definition but this is certainly how I’ve always understood it. If I was to ever start a cult I think it’d be based on militant agnostic fundamentalism.

Atheism doesn't make any positive claims. It doesn't claim to know there is no god. That's anti-theist.

Atheism makes the negative claim of: none of your god claims has sufficient evidence, therefore I don't believe them.

Now, individual atheists themselves can say and do whatever. That's on them.

This is very stupid way to put it

You have no evidence of no god.

You could disprove specific religions making specific claims, sure. But to say there is no god anywhere in the universe of any sort? That is not a claim you can prove.

Now if you want to reframe antitheists as anti-specific theology on Earth, then what you say makes sense. But you can't both propose a new definition mid-conversation, and then argue that my statement that was based on the first definition is stupid because you're using the second.

If you make a claim, you should provide the proof to support that claim.

If your claim is that "there's no gods," then you're making a claim. The assertion that there are affirmatively no gods at all is in fact just as empirically unfalsifiable as the assertion that there is definitely at least one god. In my opinion, the only reasonable position is to not make any claims about the presence or nonpresence of deities in the first place.

Russel's Teapot is fun, but I prefer Starman's copy of Treasure Planet on DVD. Do you believe that I have a copy of Treasure Planet in my DVD collection? More importantly, if you answer no, is that the same as believing that I don't have a copy of Treasure Planet on DVD? I think it would be equally silly to affirmatively assert that I do in fact have a physical copy of my favorite Disney movie, as it would be to assert that I do not in fact have a copy of it. You would have to come to my house and look at my DVD collection before reasonably making such a claim.

They have a way of making it your problem.

There is a shade of meaning between “I don't believe” and “I don’t know how a person/I could determine that they/I affirmatively believe.”

I personally would interpret the former as non religious and the latter as agnostic, but it probably differs from person to person. Especially because non religious is often used to describe people who do not practice a religion, but may well still believe in it (though that would be non practicing for me).