yankel> exempt talmidei hahamim from contributing funds to the defense of the city they inhabit .
So, it seems to me that there are two possible approaches to justify non-participation:
(1) medina is built by non/anti-religious people, many mitzvos do not apply towards them, so l’hathila there is no shared obligation, we are protecting ourselves from them
(2) halachik exemptions for Talmidei Chachamim
On (1), I appreciate historical and cultural tradition, with religious community being confronted by various ideologies. I do not think it applies to current day government and, even more, population. Israel is full of non-charedi shomer shabbos and stam masorti people, they are represented in the government, and mitzvos apply towards them for sure. Many, many of the other ones are tinokos shenishba (by earlier generations of anti-religious). These are people you will daven with together in a minyan at the kosel, so other mitzvos also apply.
On (2), maybe we can have a serious discussion what this implies. Who qualifies; what obligations and non-obligations are T’Ch entitled to; do they need agreement of others or can T’Ch demand their rights. Many, manhy questions here. For example, same Bava Basra brings an example of R Yehuda’s student who refused to admit his learning in order to get food during famine. This seems to be the opposite of the entitlement attitude.