Mozzarella in water has not bothered me any whereas even small amounts of aged cheese have.
I have been unable to confirm this but I believe that the Italians say that fresh Mozzarella contains friendly lacto bacteria.
In any case the pizza is more of a break from the monotony of the daily restrictions with either few or no repercussions. I usually make it about once every week to two weeks.
If you cannot tolerate the cheese, you can always make it without.