B"H - If IDF oath was "ALWAYS recited while holding a Tanakh in the right hand and an IDF issue weapon in the left hand", as you say, it would already be something. But it is not so in the IDF. New testaments and korans are also allowed and used. Besides, the chief "rabbi" in that organization came out in public, saying that the commander's word overrides halacha: No Jew is allowed to accept that!
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