Religious and social customs, along with familial responsibility and tradition all contribute to the community's cohesion in Things Fall Apart. What is important to understand is that what holds the community of Umuofia together are the very same things that hold together the communities of the missionaries...That is, Achebe wants us to see that the Umuofian society is intact; it has social traditions, a complex language, judicial systems, and a committment to family, not unlike any other organized and civilized community, regardless of what the colonizers might believe.
The link below describes how custom and tradition hold the community, and indeed the tribe, together - read especially the sections "Custom and Tradition" and "Culture Clash".
The community derives identity and stability through its traditions - roles are defined and accepted ways of relating to each other and the whole are clearly laid out for individuals. When the white man comes, things begin to fall apart. The "...tribe is split...the bond that ties the tribesmen deteriorates".