identifying it is a reasoning process, which they are claiming to teach.

I don't think they are. Teaching people to reason is really hard. They describe what they're trying to do as "inoculation", and what they're claiming to have is not a way of teaching general-purpose reasoning skills that would enable people to identify misinformation of all kinds but a way of conveying factual information that makes people less likely to be deceived by particular instances of misinformation.

"What about the misinformation on the atheist side!" is evidence that someone is a creationist to the extent that they cannot separate their beliefs from their principles of reason

Not only that. Suppose the following is the case (as in fact I think it is): There is lots of creationist misinformation around and it misleads lots of people; there is much less anti-creationist misinformation around and it misleads hardly anyone. In that case, it is perfectly reasonable for non-creationists to try to address the problem of creationist misinformation without also addressing the (non-)problem of anti-creationist misinformation.

I think the situation with global warming is comparable.

You're assuming I don't hold my own side to the same standards.

I'm not. Really, truly, I'm not. I'm saying that from where I'm sitting it seems like global-warming-skeptic misinformation is a big problem, and global-warming-believer misinformation is a much much smaller problem, and the most likely reasons for someone to say that discussion of misinformation in this area should be balanced in the sense of trying to address both kinds are (1) that the person is a global-warming skeptic (in which case it is unsurprising that their view of the misinformation situation differs from mine) and (2) that the person is a global-warming believer who has been persuaded by the global-warming skeptics that the question is much more open than (I think) it actually is.

then it is proof that you're looking down on the other side.

Sure. (Though I'm not sure "looking down on" is quite the right phrase.) So far as I can tell, the authors of the paper we're talking about don't make any claim not to be "looking down on" global-warming skeptics. The complaints against them that I thought we were discussing here weren't about them "looking down on" global-warming skeptics. Lumifer described them as trying to "prevent crimethink", and that characterization of them as trying to practice Orwellian thought control is what I was arguing against.

It becomes dishonest when you say "I'm just helping you spot misinformation, that's all" when what you're really trying to do is make sure that they believe Right thoughts like you do

I think this is a grossly unreasonable description of the situation, and the use of the term "crimethink" (Lumifer's, originally, but you repeated it) is even more grossly unreasonable. The unreasonableness is mostly connotational rather than denotational; that is, there are doubtless formally-kinda-equivalent things you could say that I would not object to.

So, taking it bit by bit:

when you say "I'm just helping you spot misinformation, that's all"

They don't say that. They say: here is a way to help people not be taken in by disinformation on one particular topic. (Their approach could surely be adapted to other particular topics. It could doubtless also be used to help people not be informed by accurate information on a particular topic, though to do that you'd need to lie.) They do not claim, nor has anyone here claimed so far as I know, that they are offering a general-purpose way of distinguishing misinformation from accurate information. That would be a neat thing, but a different and more difficult thing.

make sure that they believe Right thoughts

With one bit of spin removed, this becomes "make sure they are correct rather than incorrect". With one bit of outright misrepresentation removed, it then becomes "make it more likely that they are correct rather than incorrect". This seems to me a rather innocuous aim. If I discover that (say) many people think the sun and the moon are the same size, and I write a blog post or something explaining that they're not even though they subtend about the same angle from earth, I am trying to "make sure that they believe Right thoughts". But you wouldn't dream of describing it that way. So what makes that an appropriate description in this case?

(Incidentally, it may be worth clarifying that the specific question about which the authors of the paper want people to "believe Right thoughts" is not global warming but whether there is a clear consensus on global warming among climate scientists.)

crimethink

I'm just going to revisit this because it really is obnoxious. The point of the term "crimethink" in 1984 is that certain kinds of thoughts there were illegal and people found thinking them were liable to be tortured into not thinking them any more. No one is suggesting that it should be illegal to disbelieve in global warming. No one is suggesting that people who disbelieve in global warming should be arrested, or tortured, or have their opinions forcibly changed in any other fashion. The analogy with "crimethink just isn't there*. Unless you are comfortable saying that "X regards Y as crimethink" just means "X thinks Y is incorrect", in which case I'd love to hear you justify the terminology.