There are two big issues that I see, that nobody seems to want to address:
1) As charedim become a larger and larger part of Israeli society, they need to step up to the plate and take responsibility for protecting that society. That doesn’t have to involve a draft, but it does mean that SOME charedim will need to serve in the IDF, and at least SOME charedim will need to leave the yeshiva and get careers, which will require modern education. The charedi world will also have to more accept that non-charedi Orthodox rabbis can be relied upon in places like the IDF. For instance, the Orthodox rabbis in the IDF know the kashrut laws, and they have extensively researched the situations that justify chilul Shabat in the military and they can be relied upon to pasken even for charedim.
2) As charedim become a larger and larger part of Israeli society, the rest of Israeli society needs to accept that charedim are here to stay and that continuing to maintain much of that society as charedi-unfriendly is counterproductive. For example, there is no reason why charedi soldiers should be punished for quietly excusing themselves from performances of female vocalists. (I write that as someone whose own non-charedi rav is quite meikel on kol ishah.) And there is no reason why the IDF should not follow its own rabbis, who are committed Orthodox Zionists and are as upset about the unnecessary chilul Shabat as anyone commenting here.
I could list many other examples, but I think my point is clear.
I would add that the level of vitriol between charedi and non-charedi politicians is completely unacceptable — on both sides. It is time to turn down the volume. We are all one people. And the Torah of a dati rabbi and the Torah of a charedi rabbi is the same Torah even when they pasken differently in a particular circumstance.