If you were to ingest enough strawberries, they could in theory cause problems with diarrhea, though you would need to consume a very high quantity in order for this to happen.
The Vitamin C which is present in strawberries is what could potentially lead to this issue, though most people do not consume enough of them in one sitting to have that problem.
If enough of a food that has antioxidants is consumed at one time, it can actually have the opposite effect. This is why it is important to limit even healthy foods like strawberries, apples, oranges, bananas, etc. Too much of a good thing can be bad for you sometimes.