Tomas Ståhl, the study's author, summarized his findings in a statement:
“The most general take-home message from these studies is that people who do not believe in God do have a moral compass. In fact, they share many of the same moral concerns that religious believers have, such as concerns about fairness, and about protecting vulnerable individuals from harm.
"However, disbelievers are less inclined than believers to endorse moral values that serve group cohesion, such as having respect for authorities, ingroup loyalty, and sanctity… It is possible that the negative stereotype of atheists as immoral may stem in part from the fact that they are less inclined than religious people to view respect for authority, ingroup loyalty, and sanctity as relevant for morality, and they are more likely to make moral judgments about harm on a consequentialist, case by case basis.”
h/t: PLOS ONE