Liberals and conservatives disagree about obeying authorities, with conservatives holding the more positive views. We suggest that reactions to conservative authorities, rather than to obedience itself, are responsible for the division. Past findings that conservatives favor obedience uniformly confounded obedience with conservative authorities. We break down obedience to authority into its constituent parts to test the divisiveness of each part. The concepts of obedience (Study 1) and authority (Study 2) recruited inferences of conservative authorities, conflating results of simple, seemingly face valid tests of their divisiveness. These results establish necessary features of a valid test, to which Study 3 conforms. Conservatives have the more positive moral views of obedience only when the authorities are conservative (e.g., commanding officers); liberals do when the authorities are liberal (e.g., environmentalists). The two camps agree about obeying ideologically neutral authorities (e.g., office managers). Obedience itself is not ideologically divisive.It always seems to come down to definitions. What this study is suggesting is that liberals and conservatives are equally likely to display obedience as long as the obedience is to an authority which they acknowledge.
Interesting because for the past few years many sociologists have caricatured conservatives as sheeplike (obedience) and prone to falling under the spell of authoritarians. What Frimer et al are pointing out is that the original tests used definitions which were compatible with conservatives but not with liberals. If you correct for this bias and test based on acceptance of authority within your own context, i.e. authorities whom you respect, both conservatives and liberals have the same predilection towards obedience.
This is similar to some of Jonathan Haidt's Moral Foundations work. If I recollect correctly, he found that both conservatives and liberals were strongly oriented towards Fairness but liberals defined fairness as equality of results whereas conservatives defined fairness as equal rules applied to everyone equally.
Both are interested in fairness and both are respectfully deferential to authority, but each defines fairness differently and each is obedient to different authorities.