For some things, digital works great. If you’re hooking up a BluRay player to a tv, 3 feet away, HDMI is awesome. For production, it’s less than ideal.
One thing to consider is that HDMI has a maximum range (according to spec) of 10 meters (or about 33 feet). Look in your sanctuary and estimate how long a cable would have to run to get to your projector. Don’t forget that you have to go up the wall, along the ceiling, and then down to the projector. When you add all that up, 33 feet isn’t very long.
So, you can adapt the signal to SDI which will travel farther or use a set of Baluns to send it over cat5, etc. The problem is that each conversion may introduce difficulties.
Now, don’t forget that digital signals don’t show degradation like analog signals. An analog signal will slowly get fuzzier and lose color. A digital one will just disappear. So, it’s possible to have a signal that “just barely works” and it looks perfect and a signal that “just barely doesn’t work” and it shows nothing. The difference between those two looks like a lot, but in practice, it might just be an oxidized connector or a slightly weaker signal. In practice, this means that an install that “worked perfectly for months” could “suddenly quit working” for no apparent reason.