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If the property is fully owned by the Church than the rent income is not considered Unrelated Business taxable income and hence is not taxes.
Here is a link to the publication for your reference-
See unrelated business income information in the link below-
See the para for "rent" not part of UBTI in the link below
Let me know if you have any question.
Please note: This advice is provided with the understanding that all the relevant facts have been provided by you. Any change in facts might affect the advice given and hence may not be relied on in such cases. Nothing contained in this reply was intended or written to be used, can be used by any taxpayer, or may be relied upon or used by any taxpayer for the purposes of avoiding penalties that may be imposed on the taxpayer under the Internal Revenue Code of 1986, as amended.