Correct, the gods that I consider to be gods matter. The gods I don't consider to be gods don't matter as regards my atheism, attitudes towards things other than gods are irrelevant.
You have the same stance as a newborn baby towards the gods you've never heard of. Why would you be an atheist and the baby not be?
It's not an exercise in PC equal opportunity diversity management; it's purely subjective belief. Just as somebody gets the right to see whatever they like as being god for the purpose of their belief, I get the right to decide what I believe qualifies as a god for the purpose of my disbelief.
But that's not what you're doing. As soon as you start making declarations about whether people who have never expressed an opinion either way (e.g. babies) are or aren't atheists, you're appealing to an objective standard.
Think about one of the many people presumably out there who have a unique god-concept but haven't shared it with anyone. If we ignore that god-concept when deciding whether people are atheists, then we'd say this theist is an atheist: an absurd conclusion. If we don't ignore it, then how can you be said to have rejected a concept you've never even heard, let alone evaluated and rejected?
Active disbelief is just disbelief. I added the active because some people here have tried to argue that disbelief means the same as absence of belief.
Absence of belief does qualify as disbelief, so I think you need to explain what you mean better.
... but I do note that you've done absolutely nothing "active" towards any god concept that you haven't so much as contemplated.
You don't have to consider the possibility that somebody in Peru might have another 'unicorn concept' to disbelieve in unicorns. You decide what unicorns are and whether or not you believe in them.
Lulu thinks that cats are gods so she is a theist. It doesn't matter that other people don't consider cats to meet the definition of a god, what matters is her subjective belief.
I believe in cats. Lulu believes that cats are god. I don't believe in god though as cats don't fit within the boundaries of what I subjectively consider to be a god.
Ah... so you do have a definition for "god" that you use for your judgements. Good.
By your definition of "god", are Christians and Muslims polytheists, or are Pagans atheists? If your answer is "neither", can you tell us how you managed to craft a coherent definition of "god" that excludes angels but includes Pagan gods?
I just don't believe that anything I would describe as a god is real.
The same can be said of a baby.
You are adding a qualification that doesn't exist: that we create some objective definition of god. Belief is subjective though, disbelief in god(s) is in the eye of the beholder.
You're certainly imposing a definition of "god" on others when you insist that atheism be based on rejection of gods.
When it's defined by lack of belief, things are easy: conceptually, you just do a Venn diagram: as long as the "things I believe in" blob doesn't overlap the "things I consider gods" blob, then you're an atheist.