Cultural space (CS) holds significant importance for inheriting regional culture, serving people’s lives, and boosting sustainable community development. In this study, based on the research case of the Hanzhong section of the Hanjiang River Basin (HSHRB), the demand and supply matching relationships between three groups of people, namely residents, employees, and tourists, and four types of CS—memorial or religious space (MRS), cultural heritage space (CHS), cultural facilities space (CFS), and cultural industries space (CIS)—is analyzed, with communities as the units. Findings: (1) The CS demand–supply matching relationship exhibited the spatial distribution characteristics of high value balance in urbanized areas, significant lag in suburban supply, and low value balance in rural areas. (2) For the CS demands of residents, employees, and tourists, the total supply was in a substantial shortage, in general balance, and in significant surplus, respectively. (3) There were significant differences in the fairness and adequacy of the demand–supply matching of the four types of CS, with MRS and CHS more equitable and better able to meet the needs of different regions and populations. (4) Six community types with significantly different demand and supply characteristics were classified based on the demand–supply relationship within the community and the supply environment of neighboring communities. They presented a spatial structure of circles outward in the order of high-value-balanced communities, deprived communities, insufficient-supply communities, low-value-balanced communities, and shared communities, with urbanized areas as the core. Deprived communities and shared communities have shown spatial dynamics of urban expansion and village decay, respectively, and they require urgent attention. The study employs a more systematic categorization of CS supply and a more diverse perspective of demand entities, offering new evidence for the equitable distribution of cultural resources among heterogeneous groups and regions. Ultimately, it presents strategies for optimizing demand and supply as well as policy recommendations for community governance, bringing fresh insights into promoting sustainable community development.