Singing the praises of the IDF and the Defense apparatus for protecting the jewish people is akin to praising of hard snow (e.g. to build an igloo) for saving one from the cold (cf. Chazon Ish to ben Gurion).
p.s.
What about when one is obligated to serve other governments such as frum yekkes who serve in the Swiss army?
p.p.s. Excerpt from Ruth Blau, famous convert to Judaism, in her autobiography Trail to Truth.
Chapter titled My Disenchantment with Religious Zionism