I place a higher value on the method upon which people reach their conclusion (i.e. reason, logic, evidence etc.) rather than whether the conclusions they reach are correct (or whether they match my own conclusions). This is because, if someone is at least willing to base their views off the same method as mine (or society in general), we can actually have a valid discussion of the issue. A person who rejects reasoned argument and evidence as a source of truth can’t be reasoned with.
This brings us back to the original hypothetical; while the irrational atheists agree with a single conclusion I have drawn, the fact that they use an alternative method for deducing it (say blind faith; accepting a claim as true regardless of the evidence for or against it) means they are more likely to have false views in other areas (politics, science etc.). And being that the theists in this hypothetical are using reason and logic to come to their opinions, they are more likely to have better opinions in these areas. So I would much rather a world where people came to the wrong conclusion on the topic of whether a god exists or not, but were still using the preferable method of coming to other conclusions.
An analogy of what I mean can be found in mathematics classes; from my experience, teachers would give marks on tests if you used the right formulas, but made an error in calculation (and therefore had the wrong answer). Some teachers would even go so far as to not give full marks for a question if working was not shown, even with the right answer. This is pretty much exactly what I mean; it is better to use the right formula, make a mistake in calculation and come to the wrong answer than to use no formula at all and get the answer right by chance.