We use in-house deionized water in the laboratory I work at. One thing to keep in mind with DI-water is that it will rust and pit stainless steel over time. Because the mineral ions are removed from the water it tends to pull ions off the metal, resulting in the pitting.
I've only processed a couple of rolls of film so far since I'm just restarting the whole film process, but I mixed up my ID-11, stop, and fixer as well as washed with filtered water from the tap with no issues that I could see. We just have one of the under-the-sink RO systems that removes most of the minerals. I figured I'd try that first before having to buy and store bottles of distilled.