I think there are three different paths that may address these broad questions of policy relevance and societal development. For lack of better words, I will call them culturally sensitive understanding, culturally sensitive change and culturally sensitive evaluation of change. In other words: a) an examination of processes that are of societal importance and relevance, b) development and application of culturally sensitive change programs and c) a culture-sensitive evaluation of existing intervention programs so that the needs of communities are better met. Engaging with bigger questions and practical problems entailed in these three approaches can help sharpening our basic research questions and theories as well as contributing to understanding and managing global issues.
Culturally sensitive understanding of societal level problems
The first option is a focus on a better understanding of psychological processes related to important societal outcomes. There are many debates about how society can be made more humane, healthy and prosperous. What are the psychological processes that are associated with these outcomes? Here, the strength of cross-cultural psychology is the quasi-experimental nature of culture. Societies differ along a number of important outcomes and potential antecedents, cross-cultural psychologists can take these variabilities and study what variables are most likely implicated in the different outcomes across societies. An open, but critical mind about potential antecedents about potential contributing factors is important. Once certain variables have been identified as potentially important, more controlled experiments to test the causality may be conducted. Not all variables can be manipulated in experimental settings (just think of the difficulty of manipulating national histories or seasonal patterns). This option is probably closest to standard psychological research. The main difference is a closer alignment between scientific research topics and questions of practical and societal relevance.
My own focus has been more along the multi-country, sociological level of inquiry. One example is the work by Seini O'Connor. Corruption and political transparency has been on the minds of politicians, philosophers and political scientists for millennia. One of the major unaddressed questions though is what variables might be implicated in changes of corruption levels over time. There are many theories and ideas of what makes societies more or less transparent. Seini's honours project addressed these ideas through an innovative longitudinal method and found some pretty surprising findings (see http://www.victoria.ac.nz/home/about/newspubs/news/ViewNews.aspx?id=4815&newslabel=, the actual study can be found here: http://jcc.sagepub.com/content/early/2011/06/08/0022022111402344.abstract).
Implementing culturally sensitive change programs
Second, cross-cultural psychologists can engage in developing and running culturally sensitive interventions that address practical problems. Psychologists interested in culture have been relatively successful in developing and running intercultural training programs. At the same time, programs that focus on developing and changing behaviours of individuals and groups have largely been left to general psychologists or other disciplines (e.g., developmental workers, economists, sociologists, political scientists). Only few programs have taken a culturally sensitive approach when trying to change behaviours (for a cool example, have a look at this project: https://blog.itu.dk/MOSP-F2010/files/2010/03/rkhaled_siggraph09.pdf). There is much scope for innovative and important work to be done.
Evaluating interventions in culturally sensitive ways
Third, cross-cultural psychologists could get involved more in assessing existing change programs as they are applied and implemented in diverse cultures around the world. For example, micro-crediting – that is the provision of small loans to individuals or groups - has been used in many disadvantaged communities to fight poverty and contribute to economic growth. Yet, we know relatively little about the effectiveness of these initiatives, especially about how they fit in with the larger cultural norms, beliefs and practices. One of the interesting studies in this regard was reported in a study in Science last year (http://www.sciencemag.org/content/332/6035/1278.abstract) . Karlan and colleagues demonstrated that micro-crediting in the Philippines led to down-sizing of enterprises and higher stress among recipients, which is contrary to common expectations about the effectiveness of micro-crediting. This study was conducted by economists who have little interest in examining the cultural (or even psychological) processes. Cross-cultural psychologists could significantly contribute to such research and help in evaluating programs so that they better meet the needs of the communities.