I'm not sure if "looking for a theory" (do you mean an actual scientific theory or the more casual common use of the word "theory" that just means any kind of idea?) about cultural change is necessarily something of relevance to development work. Given what you have indicated your topical interest is in development work, you should look at Bob Bailey's very interesting work encouraging adult male circumcision in Africa to decrease transmission of HIV. He has a page here on RG (Robert C Bailey). Many of the projects he has spearheaded that have reduced HIV transmission required promoting different ideas about circumcision than were common in areas suffering from high HIV infection rates.

not sure if Robert C. Bailey's page here on ResearchGate is being identified in my last answer - search for Robert C. Bailey, Ph.D. MPH, University of Illinois at Chicago for his page.

One theoretical approach that I have found helpful is the idea of societal frames. In a piece from a while back, Hank Johnston argues for three levels of discourse: representative, frame-aligning, and everyday. In many cases local knowledge is treated as representative and thus authoritative. Ideas from outside the society may not enjoy the highest status.

Johnston, Hank. 2002. 'Verification and Proof in Frame and Discourse Analysis.' in Bert Klandermans and Suzanne Staggenborg (ed.), Methods of Social Movement Research (University of Minnesota Press: Minneapolis).

Although I haven't personally dealt with the question of development that much to be able to offer a comprehensive overview of theories (in both sense of the word), one book that comes to mind is: Merry, Sally Engle. 2006. Human Rights and Gender Violence: Translating International Law into Local Justice. Chicago: Chicago University Press (Chicago Series in Law and Society)

In it, she deals with the question of implementing laws regulating violence against women in Hawai'i, Delhi, Beijing, Fiji, and Hong Kong, stressing the role of NGO (and other) activists who serve as intermediaries, translating human rights law from the global to the local. By analyzing their roles, she gives a theory of how outside concepts are framed in order to be adopted by the local population, without losing their radical edge, so to say.

Since you're dealing with attitudes towards FGM, this might be more useful to you than works on development that focus on infrastructure and other technical innovations.

Whereas there is no exact theory I know, you can look at the socio-ecological theory to explain how individuals ( mutilated girls) are affected by their environment at various levels. And then, chip in conflict theory to explain how this issue is being accepted or not in the area. Finally, look at diffusion of innovation theory to help you explain how change is accepted. from early to those who never do. Afterwards, you can draw from the literature and the piecemeal theories to create a conceptual framework that will fit the exact message or understanding of the issue in your context.

Ellen Gruenbaum (Anthropologist, Purdue University) has done a lot of work on change projects and Female Genital Cutting (and the politics of labelling 'cutting' vs. 'mutilation'. Her work might be of interest to you.

Hello Therese. Your question is at the heart my own research on connecting across cultural boundaries in development work. One book I’ve found helpful, although heavy in places, is Paul Hiebert’s Transforming worldviews: An anthropological understanding of how people change. This book identifies a lot of spiritual and religious assumptions that underlie how different groups think, leading to ontological approaches to change. You might be aware of successful transformational work being done at the coal face on a range of health issues, adopting Hiebert’s spiritual and religious theories, and building bridges incrementally.