According to a recent theory, public opinion on moral issues will trend toward opinions that are justified by generally acceptable kinds of arguments. Both in the United States and the United Kingdom, generally acceptable kinds of arguments include concerns about harm, violence, fairness, and liberty. The theory therefore predicts that these countries will exhibit similar opinion trends on moral issues. We test this prediction using polling data on 98 issues in the United States and 108 issues in the United Kingdom, with an overlap of 27 issues on which opinions have been polled in both countries. We find that moral opinion trends are well predicted by the applicability of generally acceptable kinds of arguments and that there is a remarkable similarity between opinion trends in the two countries. These findings lend support to the theory that generally acceptable kinds of arguments play a key role in driving opinion dynamics.