Excerpting from the Steipler’s letters [click the various tabs on the page to navigate], bolding added (the page is somewhere around 219-221, to be updated soon):
“My humble opinion leans towards the view that it is a great mitzvah to vote for the chareidi list and that this constitutes the saving of religion . . . as for your argument that there are [Torah] prohibitions involved, I have given great consideration as to whether it is worthwhile responding because in truth, it is utterly against my wishes that the members of Neturei Karto, sheyichyu loy’t, should change their opinion. Whilst no prohibition is involved in voting, there is zeal for Hashem’s sake in their refraining from doing so.“
NOTE: I hope to provide the actual original quote soon, but this quote is largely accurate, as I recall. (Adjacent letters contain other reasons for not wanting to disagree with the Badatz, but this doesn’t take away from the above!)
Of course, needless to add, had the Steipler examined the Manifesto be’iyun, he would have gone even further… Of course. Needless to add.