I did not read all the responses, although the OP touched on a number of potential answers. I’m sure the usual suspect answers were already given and if not, will surely be debated to death over the next few days or until someone crosses a line and the moderators are forced to shut the thread.
To answer the OP. I personally daven in a shul that does not make a mi shebeirach for the Tzahal, this does not make me, or those who daven in the shul anti the medina, or kofui tov to the Tzahal. I can not speak for anyone but myself here. when I daven for the well being of klal yisroel in galus, in the bracha of goel yisroel or when we say sim shalom…”val kal yisroel” it includes all members of klal yisroel, not specific members.
You say a special teffila for the Tzahal, thats your perogative. Do you say a special tefillah for the cholim in your local hospital? If not, does that mean you could care less if they just drop dead?