You keep using the phrase "the church;" is this person running their own church? That's what is confusing. They run their own church; or they work for a church? Or, you have two different churches, and the other church pays him as an employee on W2, and the Sched C is for the SE part of that job?

As a Sched C filer, he won't have someone else's ("the church's") equipment on his own return. He would have his own equipment on his return, for doing the other work or, his business associated with being an independent minister not working for "the church."

That's where this gets confusing.