People often justify their moral opinions by referring to larger moral concerns (e. g., “It is unfair if homosexuals are not allowed to marry!” vs. “Letting homosexuals marry is against our traditions!”). Is there a general agreement about what concerns apply to different moral opinions? We used surveys in the United States and the United Kingdom to measure the perceived applicability of eight concerns (harm, violence, fairness, liberty, authority, ingroup, purity, and governmental overreach) to a wide range of moral opinions. Within countries, argument applicability scores were largely similar whether they were calculated among women or men, among young or old, among liberals or conservatives, or among people with or without higher education. Thus, the applicability of a given moral concern to a specific opinion can be viewed as an objective quality of the opinion, largely independent of the population in which it is measured. Finally, we used similar surveys in Israel and Brazil to establish that this independence of populations also extended to populations in different countries. However, the extent to which this holds across cultures beyond those included in the current study is still an open question.