Rav Raffi Feurstein one of the founders and Chairman of the Board of Tzohar has published an opinon piece in Ynet, detailing why he didn't fast yesterday. As opposed to Harav Moshe Lichentstein on whom I blogged yesterday, it seems that his main point of contention is that the Chief Rabbinate is irrelevant. He points out that the Haredi communities do not listen to the chief rabbinate, and were on the whole unaware of the call to fast yesterday. He (correctly) points out that the only community that still cares about a ruling by the Rabbinate is the Religious-Zionist community. However the Rabbinate ignores that communitie's institutions, and as such has little influance over them.
In his words it is a Rabbinate without followers.