I quote the Catholic News Service Stylebook on Religion. Think of them as a religious version of the Associated Press Stylebook.
church
Do not capitalize unless it is used as part of the formal name of a building, a congregation or a denomination. Holy Redeemer Church, the United Methodist Church.
Lowercase in plural uses when two formal names are combined: Trinity Lutheran and Holy Redeemer churches, the Catholic and Methodist churches, Orthodox churches.
Lowercase church when it is used in an institutional or general theological sense: Father Smith said the church will not ordain women. The church is the people of God.
In references to local Catholic entities, generally use church for the building, parish for the organization and its people: The roof of St. Odilia Church was destroyed by a tornado. Members of St. Odilia Parish raised the money for a new roof in two days. It is also correct, however, to use church as a synonym for parish in such contexts: the members of St. Odilia Church.
Use a possessive form (for example: St. Mary’s Church) in a full name only if it is officially in the formal name. For names of Catholic churches in the United States, consult the Kenedy directory.
Catholic News Service (2013-02-22). CNS Stylebook on Religion: Reference Guide and Usage Manual