Spelling out membership in the Unitarian Universalist Association (UUA) in a congregation's bylaws clearly defines the congregation as a Unitarian Universalist congregation. It can also serve to prevent leadership from removing the congregation from the UUA without consent of the congregation.
Some congregations also refer to their membership in their particular district or other affiliated organization. Because of the flux of organizations, it would be wise to include words such as "or its successor." It is always a good idea to amend the bylaws to reflect new names of the organization, though with a successor's clause it need not be done immediately. It is also wise to ensure that the formal legal names of such entities are used.
The (Congregation/Church/Fellowship) shall be a member of the Unitarian Universalist Association of Congregations.