A qualifying church is not required to file an annual informational return (Form 990). Would this change if the church owns a single member LLC? Assume that unrelated business income tax (UBIT) is not as issue.
Great question and a new one on me! But it seems that its qualification under the church and its exemption falls under the Group Exemptions provisions of the Internal Revenue Code. Specifically, whether the LLC is a "subordinate organization" will likely determine its inclusion under the church's filing waiver. IRS Publication 4573 (link below) seeks to define the qualifications and may be helpful.
IRS Pub 4573
As the inquirer points out, the UBIT matter is important. Churches earning unrelated business income must file Form 990-T and pay income tax on any profits.