I just found this little list about why you should avoid coffee. #3 is what increases intestinal permeability (leaky gut). #2 is extremely significant if you’ve suffered from any long bouts of stress or still suffer from irritability, aggression, negativity, or anything that habitually sets of a stress response. I don’t know how this varies if your coffee is fake though.
I was drinking decaff before the diet, and I found it a lot less harsh on my stomach. It could depend on the brand, but it might be worth trying to get yourself off the caffeine before giving it up completely. I assume you like black coffee, by the way? I don’t think there’s any milk substitute allowed on the diet.