Firstly my name is Vincent, I head the worship team and oversee video production in our church.
Recently within the last year we started running stereo backing tracks at church through mainstage. We have an Audio Interface outputting 3 channels of audio, One Stereo Track left & right, and 1 channel with Click & Song Guide combined being outputted separately to the sound board and through our aviom in-ears. In Mainstage we have the tracks grouped together in playback and cued with a single button on a midi controller. Now that's just if we're running tracks without video.
Now onto adding video to equation. We use software called QLab, this thing is absolutely the best. We sync the video up in Adobe Premiere to our backing tracks to ensure things will sync up in QLab correctly. We export the video without audio and import it into QLab just in case we want to interchange keys for different worship leaders. We import the Stereo Track, then the Click with Guide into QLab separate and route them through the same audio outputs that we'd use if we were just running audio in mainstage. Then once we get that all set up then we set the video and all audio tracks to be cued by a midi note on a controller and bam there you go video synced with music. By the way all this is being run on stage by our keyboard player.
To output video from the iMac we have a thunderbolt to HDMI converter on stage and set the video to outputted to pretty much a secondary monitor that is the camera switcher. Theres a lot of tutorials on QLab & Mainstage but knowing the software name is 90% of the battle. I hope this helps you, your church, band, or whatever else you have going on.
Lastly I truly believe that if we have information that is useful or helpful and has been a labor to find, we should share it and make it more accessible for other churches or just people willing to learn about something. I heard this somewhere and it may even be a scripture somewhere but I loved it, "God's house should be the best because our God is the best." I live by that thought day after day and I believe if we have information that can help make THE church as a whole the best it can be why not share a little bit of useful information that was stumbled on.