Eaton has several traction aids that can be problematic with synthetics. So do other traction aid manufacturers. It's mostly to do with those that use friction as part of their functionality (limited slips). The unit is designed to operate with the friction characteristics of a certain oil and when you install a synthetic with friction characteristics that differ greatly from the calibration oil, the unit doesn't work as advertised (typically a lower the bias ratio) or is noisy. To my knowledge, the E-Locker isn't one of those, nor would be any mechanical unit like the Detroit belikely to have a problem, but the Trutrac and some other limited slips are "no syn." They really don't want to test every combination of oil so they deliver the blanket, "No syns." In the case of a "no syns" unit, you can either have the advertised functionality and the full warranty, or synthetic oil. Definitely a factor in which unit to buy. Given that there are so many good mineral oils out, it isn't a huge factor IMO, but it might be for some.
I believe they could reengineer all the problematic units to be more suitable with synthetics, but that costs money. With one limited slip I know of, there is a permanent reduction in bias ratio that can be done by using synthetics long term.