As a fruitarian I trend not to eat different fruits together during one meal; instead I will have 3-4 avocados for instance and another fruit about 1 hour after, such as 20 or 30 tangerines. Simply because it takes me at least 30 minutes to digest the "previous" fruit, sometimes more, depending on the quantity and water content.
However Dates and Bananas go so well together. I think this is not a terrible deal as they both are part of the same subcategory of "sweet fruits", as such, the enzymes secreted to digest these are somewhat comparable, and certainly not "incompatible"; at least, that's my understanding of it and I'm not a nutritionist. A bad combination would be, for instance strawberries and bananas, as the enzymes required to process these are mutually canceling eachother, making digestion (and micro nutrient extraction) more difficult.
This theory is very easy to test, combine avocados and nuts for instance and tell me how easy you can digest this. Good luck!
Anyway, do you think that a fruitarian should not mix bananas and dates together, or is this an acceptable combination?