I don't think studies like this are helpful because people groups are not monolithic. In my experience, I have been around progressives who are not just intolerant but downright mean-spirited towards conservatives, dismissing them as stupid, ignorant, rednecks, that kind of thing. I have also been around conservatives who are hateful towards progressives. The reverse is true as well, and far more often.
The dominant experience in my life has been with people who are relatively kind and well-meaning, even if they disagree. Much of my current church is comprised of staunch conservatives. They know that I am not. We get along fine.
In a very unscientific perusal of my Facebook feed, it seems that my more conservative friends are more likely to post comments and stories about "snowflakes" or "stupid liberals" that attack progressives as a group, whereas my progressive friends are more likely to post comments and stories directed at a specific issue or position rather than at conservatives as a whole.
Intolerance is not the prerogative of any political party or group. It's irrelevant to me whether one is more or less intolerant than the other. We need to focus on trying, within reason, to eliminate aggressive, hateful intolerance altogether.
Short answer: I do disagree with the study if it is used to infer larger generalizations. (It is not really the way that all studies are done in that they did not attempt to create a nationalized, representative sample).