I thought the other groups were also to varying degrees anti-Zionist. Though nothing is terribly clear.
The best way of looking at this is probably at surface value, that they oppose the draft because they are caught up in a sectarian ghetto mentality, and know that if their children see other situations (and “the big city”), they won’t want “to go back to the farm.”
But it’s a losing argument from two perspectives. The first is that having a military and keeping order are the two primary functions of government. If they don’t support the military, they have reneged on the social contract.
The other reason is that yes, while there will be attrition of some of their children, others will return, and likely with ideas that will revitalize their communities.
The Satmar do not believe in a social contract, a concept which they would associate with the secularism of the Enlightenment.
They believe in a covenant between themselves and the Almighty, and they reject any entity or organization that they think interferes with their observance, including the government.
The other reason is that yes, while there will be attrition of some of their children, others will return, and likely with ideas that will revitalize their communities.
They do not believe that any ideas that come from sources outside of their community have any vitalizing effect on them.
If it comes down to it, they would rather pay jizyah again than have the Israeli government intrude upon their personal lives.