I would hesitantly say it probably would. They didn’t include that in the scan, but did in the self reporting questions. And found no real difference in either groups self reported empathy toward the other group.

Furthermore, at the self-reported level, we assessed inter-group empathy levels (toward rightists vs leftists), and our results did not reveal any significant difference between the two groups, and rather moderate levels of empathy toward each other.

That combined with the starkly increased measured of empathy for others generally, which was more pronounced than self reporting showed. It would make sense that the same pattern continued, even for the opposite associated group. I would expect rightists to be less empathetic to leftists than self-reported, and leftists to be more empathetic to rightists than self-reported.