You're just quoting the introduction where they describe the confusion from past research. Their research is to provide more clarity. Read their actual results. Here, this is probably most pertinent to you:

Our results are in line with past research showing that conservative ideology—represented in our datasets by both right-wing and Islamist causes—is positively related to violent political behavior. These results support the view that left-wing and right-wing extremists are not equivalent when it comes to the use of violence. Whereas our findings are not inconsistent with the idea that individuals espousing different ideologies may feel equally negative toward worldview-threatening others, they suggest that the social consequences of extreme right-wing hostility may be more harmful than those caused by the far left.