religious affiliation
A place operated by or connected closely with one particular religious faith.
A religious affiliation is applied to a place that has a direct connection to some religious organization, tradition, or faith. This is applied to places such as hospital, schools, mission houses, community centers, orphanages, religious housing, assisted living facilities, or graves. It does not cover churches, synagogues, etc. which already have their affiliations included in the usage.
The connection can concern operation, ownership, or a direct association with the faith or its organizations. The place can serve a non-worship function while retaining that religious connection.
A house of worship whose use already identifies its faith falls outside this additional affiliation distinction. Religious affiliation also differs from an honorific or hierarchical designation such as cathedral status.