In this context, "at their disposal" means that family culture is the most significant and readily available resource or tool that sociologists can use for their research. It implies that family culture is a valuable and abundant source of information and insights that sociologists can draw upon to study and understand various aspects of family dynamics, relationships, traditions, values, and behaviors.
By studying family culture, sociologists can gain a deeper understanding of how families function, the roles of different family members, communication patterns, shared beliefs, rituals, and how these factors shape the experiences and lives of family members. Family culture provides a lens through which sociologists can analyze social structures, norms, and the influence of broader societal forces on individual and collective family behavior.
In summary, "at their disposal" means that family culture is a crucial and accessible tool that sociologists can utilize to study and interpret the dynamics of families in society.