Issue #1 here is that the amygdala is implicated in emotional processing in general, all emotions. The journalist's assertion that it's the "fear center of the brain" is pop science; it's a lot more than that. If you look at the study, the authors don't state that conservatives are the way they are because they're fearful or anything like that, but that there's a link between brain structures and political affiliation. It's the journalist that's using deceptive wording to paint a negative picture. The amygdala has been extensively studied in regards to fear processing because it has clinical implications, e.g. anxiety disorders, depression, PTSD, etc, which is probably why lay people tend to associate the structure with it. Scientists have rarely done research on the positive emotional states related to it.
There have been cases of people who suffered damage to their amygdalas, which can be used to infer what the structure might do. Researchers observed a few things about the behaviour of these patients. They were overly aggressive and sexual, they routinely put themselves in very dangerous situations without a care despite having normal intelligence levels, they had excessive trust towards other people, they had oral tendencies (putting stuff in their mouths...) and they displayed very little emotion. They also had great difficulty reading the facial expressions of others (they couldn't identify joy, fear, etc) and rarely looked into the eyes of other people. You're looking at a general handicap in terms of emotional processing, appropriate behaviour in terms of aggression and sexuality, and survival (inability to recognize threats). If someone had a bigger amygdala, if anything they might be more "switched on," like the opposite of an autist, someone that's more aware of the emotional states of others and their environment in general.
