The reason behind this is quite interesting, really.
The mod adds a new item to the game (their 0-cost converter stand-in) with the name #CONVERTER_NAME (because they just copied the real one). For EID, seeing a name in this format changes how EID obtains the item's real name, falling back to other options. But of course, the fake converter doesn't have a fallback to go to.

So, they need to change their fake converter's name to something else. (You could do so on your end by modifying the converter mod's /content/items.xml, and also changing the Isaac.GetItemIdByName("Converter") line in main.lua)

The recipe list is failing when I pre-sort every item's name alphabetically; technically, this fake converter isn't in any item pools and therefore would never be a recipe result, so it doesn't need its name checked, but I'm not changing the code over this. You can duplicate the error by spawning the fake converter on a pedestal in debug console.

Just to update, looks like the dev for the other mod is going to implement a fix for this in their next update. Thanks for being so in-depth Buurazu!