I watched this video when it came out and I disagree with the findings in it, because to me it seems less to indicate that people reject logic because of political affiliations, and more people are critical of studies that contradict prior knowledge.

People interpreting results on the skin cream have absolutely no frame of reference. There isn't a brand name associated with the skin cream that might have some kind of recognition for people to have prior knowledge. The study that they are presented with is the first time they are seeing anything about this skin cream.

People weighing in on gun control, have a lot of prior knowledge on the topic. Now whether all this knowledge is based on facts or data is obviously questionable. But regardless they have prior experience with the topic. So naturally you are going to be critical of a study showing you results that directly contradict your prior knowledge. Also from the video it doesn't seem clear that they are asking them to specifically treat it like math problem and make judgements based on the study alone. They are asked whether they think gun control is effective. And while obviously they have the infographic right in front of them, most people are not going to base their judgements solely on that data alone.

To put it another way, what if the study was based on something non-political, like say whether smoking 2 packs of cigarettes a day improves or worsened lung capacity over the course of a decade? I think most people would be heavily critical of the study that shows smoking improved lung capacity even if the data they are presented reflects that. And I don't think it would be because they are simply rejecting logic and numeracy based on affiliations. It's because they have prior information and knowledge that directly contradicts the singular study that is presented to them.

And this is ignoring the fact that while the statistic they use to measure the effectiveness for the cream is very tangible and direct. Either the rash improves or it worsens. And you can make direct comparisons with the control groups. In the gun control study you are comparing different sets of cities, ones that have gun control laws and ones that don't. You aren't comparing the same set of cities before and after gun control. So already this is a poor study. Then to make matters worse the statistic they use to measure the effectiveness is "crime worsened" and "crime improved". Not crime committed with firearms. Or even just violent crimes. Just crimes. And in cities where gun control laws have been implemented, crime is naturally going to go up because there is a new law for people to break. Anybody who isn't following the gun control laws in that city are committing a crime whereas people in the cities without those laws are doing the exact same thing, but it's just not counted towards "crime" because it hasn't been outlawed.