The AVB networking protocol only works through AVB approved switches/devices. Most of these switches are of the un-managed type. Your AVB setup will probably need to be separate from any other networking in your church. Sometimes, this type of networking is called a "closed-network". All the AVB network cabling will need to be of decent quality, including anything you would put in the walls. You should be able to connect from the console to your switches using networking ports at FOH and at the stage, however, even these ports may need to be of higher quality.
Check the AVB protocols and approved devices before actually conducting any work.