what does this departure from Zionism really mean in more practical terms? It means, that one is not in rejection of a democratic, secular state, a state that is not a “Jewish state”, but that accepts Jews as Jews, as it allows religious freedom, as it separates religion from state. That’s all.
That's not all. Meretz supports a secular state. The discussion about which powers, including none at all, the Israeli state church should have occur entirely within a Zionist framework. The Status Quo Agreement (https://books.google.com/books?id=iVJR9UZnTVAC&pg=PA58&lpg=PA58#v=onepage&q&f=false ) was an agreement reached because 1940s Zionists were divided on the role of religion. It is likely the majority of 1940s Zionists opposed any role for a state church but at the time simply didn't want to fight that battle. The Israeli state doesn't need a Jewish state church more than France's move away from state Catholicism caused the state to cease to be French.
Anti-Zionism is a desire to destroy the Jewish nation, not a desire to reform the Jewish state in any way including religious relations. A series of political reforms which left the Jewish nation intact and secure while merely changing some laws would be a failure of anti-Zionism not its completion.
Let's pick another example to make this easier. Ireland has for the last 150 years been slowly weakening their state church. One can support Catholic control of the education system, support the church's influence or oppose either of those things without ceasing to be a supporter of the Irish Republic. The equivalent of an anti-Zionist would be someone who supported Cromwell's policy of England conquest and the settlement in Ireland of a non-Catholic population. The equivalent of anti-Zionism is opposition to the Irish nation, not just opposition to particular state policies.