“The gedolim will say sure it’s a mitzvah to protest, but I am sorry, it’s a bigger mitzvah to daven to for yeshuosh”
I’m also sorry for you
It’s one thing to thing you know better than the gedolim in worldly matters but how can you thing you know better than them regarding what’s a mitzvah? Do you also think you know more about heart surgery than a heart surgeon ?
That’s not just a question of emunah it just make any sense to think that
Btw it is true that all the gedolim have said in the past to protest including R Elyashiv R Shteinman and R Chaim Kenievsky however not all agree in the specific case of the draft issue
Also I’m sure you yourself would have a point were you feel an injustice is great enough to protest for example clear anti Semitic acts by a government or the like despite that protest inconveniencing others it’s simply a question of values for these people spiritual persecution is worse than physical (that also happens to be the Torah’s view as the Gemara states: it is worse to cause one to sin than to kill him