LMA – The wording of the mi sheberach does give legitimacy to the zionist institutions. Hence it cannot be recited. Your point about the zionist entity existing regardless whether we recite it or not is meaningless. Would you therefore recite a misheberach for the Cuban Communists since you feel whether reciting it or not is without effect?
The State has caused a lack of security by inciting the Arabs to violence against us. And the State does not provide as much financial assistance to us, as we (Torah Jewry) provide financial assistance to the State in the form of taxes, fees, and all sorts of regulatory stuff.
And reciting the mi sheberach will do nothing towards feelings of the frei. The religious zionists already say it; the Shiuni-types hate us nonetheless. They will not be appeased “only” until the last Neteurei Karta Yid says the mi sheberach.