We are confusing several distinct issues.
One involves conscription of those who hold that the war is not allowed by halacha (neither milchemes rashus nor milchemes mitzvah) meaning that Israeli soldiers are required to refuse to kill goyim or destroy their property (i.e. we are the rodef, they are the nirdaf). If you hold that way, which is what anti-zionist hareidim hold, it is irrelevant whether you are in yeshiva, you must refuse to serve in the army. In the past, this group, perhaps a tenth of hareidim, but perhaps more, were exempted under the theory they were learning. Given Israel’s non-recognition of conscientious objection, they now have a serious problem (probably solved by allowing Jews with halachic objections to military service to be exempt, similar to how Arabs Muslims are treated). Non-zionist hareidim will probably prefer prison, if drafted will be very bad soldiers, and will complain to international human rights groups if drafted.
There is another issue of funding yeshivos (hareidim don’t want government funding, zionists think it is proof that Israel is a Jewish state), compounded with the fact most hareidi males are banned from working (“on the books”) since they haven’t served in the army. Almost no one in Israel supports a continuation of this policy, and from an economic perspective, it is hightly dumb.
Then there is the position of many pro-zionist “hareidim” who support having other people bash Arabs heads, but want to learn gemara themselves. These are probably hypocrites. In America we call them “chicken hawks” – pro-war, but not wanting to serve.
Lastly there is the problem of the IDF encouraging, tolerating and sometimes activitly persecuting hareidim who do serve. Regulations and policies to prevent this are ignored. At best there in segregated units (similar to the American Buffalo soldiers, or the British native regiments). The only solution for this is to tell officers that if they can’t keep all their soldiers happy and working together amicably, meaning hareidi soldiers shouldn’t feel they have to give up on mitsvos to serve – they’ll be replaced by officers who can (note that when someone scheduled female singers for a ceremony, the officer was praised widely rather than told to find a different line of work).
These are all separate issues.