Hakatan: Our support through citing Mi Sheberach, in reality can hardly be considered support for the State at all, since the State of Israel will exist regardless of our symbolic and indirect endorsement of Her. Therefore your argument to consider the act of Mi Sheberach as being “Mesaya L’dvar Aveira” has hardly any substance.
And, From a Torah perspective, we probably have a moral obligation to express our hakaras hatov to the state through citing the Mi Sheberach. Have they not provided us with real security and financial assistance for the past half century? Were we not taught in the Torah that hakaras hatov is of the most primary moral obligations of a human being (Moshe Rabbeinu with regard to the earth and sea of Mitzrayim)? Where are those genuine human feelings within you? Have they become lost within your sea of hatred for the State?
Additionally, if it were actually assur to express publicly an indirect endorsement of the State, then it would definitely be also assur for the Chareidim to have representatives in the Israeli Cabinet, since this also constitutes an indirect endorsement of the State; especially with taking actual monetary assistance from the State’s treasury.
The real reason for your reluctance to cite the Mi Sheberach stems from your feelings of pride, and your unwillingness to publicly express what may be perceived as a concession to the State. Well, if you felt your moral obligation of hakaras hatov, then that should override your other feelings of hesitation to cite the Mi Sheberach. And trust me; if you and others would publicly cite the Mi Sheberach, it would come a long way with sending a conciliatory message to our irreligious brethren in Israel, and you never know how many more Jews would become closer to Yiddishkeit as a result of this.