I gave a few basic criteria earlier (e.g. that a god is an intelligent agent who has a will and acts on the basis of that will), but in the end, I think this problem is for the theists to solve: it's the person claiming that God exists who needs to justify why what they're calling "God" would actually be God... and then, of course, it's up to them to show that the evidence supports their claim that this thing exists.
I guess I am adopting the perspective that worship is the defining entity. "Gods" and "deities" are just too vague in and of themselves.
So then every believer who believes that their god or gods are gods on the basis of some sort of objective criteria are necessarily wrong? It seems that this is the implication of what you're saying.
No, actually I am claiming that they are right because they choose to be right in that specific way.
They become wrong when or if they attempt to apply the same criteria for others without their own agreement, though.
There are plenty of theists who believe that their god(s) exist on the basis of some sort of objective evidence (or at least what they consider to be evidence).
Indeed. Many are deluding themselves, either about how much sense it makes to talk about objective existence of deities or about how much importance it is for them to exist objectively at all.
It is not all that rare for them to be self-deluding to some extent or another. That is often not a problem, because self-delusion
can be a legitimate and useful religious practice, to the extent that it brings direction and motivation.
The trouble exists when one gets too attached to the tool that such delusion is. But when correctly contextualized, self-delusion is fine. It certainly beats the rather puerile approach of simply assuming that what one believes in is Truth Itself and plan all of one's choices as a function of that. That approach forbids itself from finding better understandings and ends up in an unending, often paranoid spiral of even growing self-reference and avoidance of outer input.
My approach has generally been to dispute their claim on the basis of the evidence, but it seems like if I adopted your view, I could reject all these claims without really examining them
That you can. Everyone is entitled to reject any claims of existence of deity they feel like, even randomly and without attempting any justifications.
on the grounds that since gods aren't justified on the basis of evidence, if they're trying to justify their god with evidence, then their justification is necessarily invalid.
Not invalid. Irrelevant, or perhaps unapplicable is a better word.