When is a Religious Belief Delusional?

[Angrboda]

The definition of a belief is an acceptance of something as true or that something exists.  How can you be wrong without holding something as true?

Synonyms are: wrong, mistaken, in error, incorrect.

I was lost and made a wrong turn.

First of all, this is not about a person being wrong, but a turn being wrong. A turn is a thing. Things simply can't hold beliefs and the discussion wasn't about things but persons, so this example is irrelevant to the conversation. We're interested in the difference between a person being wrong and a person being deluded. Second, you've equivocated here. The sense of wrong under consideration is that which is the same as mistaken. You wouldn't say he took the mistaken turn, so obviously you're appealing to a different meaning of wrong than that under discussion. So this is not an example of a person being wrong rather than deluded.

I didn't know that so I was mistaken.

In order to be mistaken one has to be mistaken about something. If a person doesn't have a belief about something and one is just ignorant, then it is not appropriate to say they were mistaken. The only way not knowing could be relevant here is if they didn't know something relevant to a belief they had. Otherwise they are not mistaken because there is nothing they were mistaken about.

Not covering my sneeze was incorrect.

Not covering one's sneeze is an action. It's a thing. So the person isn't mistaken for not covering their sneeze unless they had an opinion or belief about the appropriate behavior. The action of not covering one's sneeze being defective in some sense is again irrelevant to the discussion of persons being wrong or mistaken, in the same way as your first example.

I made an error in counting. 

How does one count without beliefs about the number of things one has counted? Unless counting is something you can do without having any beliefs, it's not an example of a person being wrong without beliefs. Unless you're talking about, say, a person using a clicker to count off inventory. In that case, again we're dealing with actions rather than persons being defective. So it wouldn't be relevant. (And you're probably equivocating here as well, as making an error is an action and actions are incorrect in the sense of being defective, not in the sense of being mistaken. Actions cannot be mistaken because actions don't think.)

None of these need a belief, or at least the same kind of belief as religion/theism.  I doubt that you can substitute delusion in the above statements.

Half of your examples do in fact need a belief, and, in the sense you are using it, deluded most certainly could be substituted for the relevant expression of wrongness. In the other half of your examples, the thing that is wrong is not a person, so it's not a relevant example.

I don't know that you can't give an example of a person being mistaken without holding a belief, but so far you have not done so.

As far as we can tell from the examples you've provided so far, your distinction that delusion involves a belief where being mistaken does not appears to be incorrect.