Since you were talking about values in a political context, I assumed they were political values, which usually presuppose some facts. Policies are rarely preferred entirely deontologically.

Do you have specific examples of the values you were referring to?

I said that when I look at a European country, I see a bunch of parties strung out along a left-right axis. But, actually, I guess I don't see anything, I just hear people describing the parties that way. Say, a left party L, a center party, C, and a right party R, allowing LC and CR coalitions. But often, when I look closely, they do seem to have exotic platforms that shouldn't rule out the LR coalition. For example, people were shocked by the British Liberal Democrats forming a coalition with the Tories, because "everyone knew" that they were a left party. (I guess everyone knew that because the Liberals and Social Democrats used to be left-wing, but somewhere along the way the Liberal positions because right-wing.) Similarly "everyone knows" that anti-immigrant parties are right-wing, and that it is completely impossible for them to form coalitions with left-wing parties, but most of them are single-issue parties with little opinion on anything else, certainly not a right-wing positions. (But they can’t form coalitions with anyone because they are anti-establishment.)

And, similarly, it is odd that the Slovak libertarian party is labeled “extreme right-wing” seeming to rule out the possibility of including it in a left coalition giving it control of civil liberties.

you should never think that any position of someone who disagrees with you is based on motivated reasoning.

No; I didn't say that and if you think you can infer it from things I did say then at least one of us has made a serious error.

What I do claim is: (1) the mere fact that their position matches their values is not sufficient ground for thinking they're engaged in motivated reasoning; (2) motivated reasoning can happen (and does happen) on both sides of any issue and you shouldn't assume it's only on one side.

the positive claim is the one that needs to be analysed for motivated reasoning.

This is at best a heuristic (just as e.g. the notion of "the burden of proof" is). The same claim can often be cast as "positive" or "negative" without changing its content, and any claim (positive or negative) may be the result of motivated reasoning. (Stefan's paper gives right-wingers' skepticism about global warming as an example; in this thread you give left-wingers' endorsement of global warming as an example; I bet the amount of motivated reasoning going on in both cases is non-zero[1].)

[1] The amounts may be very different in the two cases.

Let's take a more careful look at your example of creationism. It is absolutely correct that "evolution is a conspiracy of scientists" is convenient for creationists, and that "evolution is not a conspiracy of scientists" is convenient for evolutionists. We can flip them around so that "positive" and "negative" change places: "evolution is an extremely well supported scientific theory and is almost certainly correct" is a positive claim. (You may notice that evolution and climate change fit the same templates.)

So the "positive versus negative" test is no use here. What else can we do? We can investigate the matter thoroughly for ourselves (in which case we no longer need to care much whether other people are engaging in motivated reasoning). We can look for less-biased populations, as I did two comments upthread, in which case we'll find plenty of devoutly religious people and non-scientists who accept evolution and very few devoutly irreligious people and scientists who reject evolution; and we'll find that in places where evolution is less "politicized" (meaning, in this case, less used as a shibboleth in arguments about religion or about the prestige of science) it's very widely accepted.

Or we can do what Stefan's paper describes (which overlaps with what I describe), and look at the extent to which people's attitudes to evolution are part of a bigger picture where whatever's hypothetically motivating them motivates other things too. Do anti-evolutionists tend also to be anti-abortion, anti-same-sex-marriage, (in the US) Republican rather than Democratic, etc.? Why, yes, they very much do, which by Stefan's heuristic suggests that their anti-evolutionism is likely to be the product of their religion. Do evolutionists tend to have positions opposite to those? Probably yes, but not to nearly the same extent.

What if we consider not religion but "prestige of science" as a possible cognition-motivator? Do evolutionists tend to accept anthropogenic climate change, quantum mechanics, general relativity, heliocentrism, etc.? Yes, but most of the things hidden under the "etc." are more or less uncontroversial, and on the actually-controversial ones (e.g., climate change) my prediction is that again we'll see more alignment with allegedly-motivating beliefs on the creationist side than on the non-creationist side.

So, it looks to me as if we can do pretty well at telling whether creationism or its reverse is more likely the result of motivated reasoning, but we need to work harder to do so than just decreeing one of them the "positive" position. Likewise with climate change. Do you disagree?