If anyone suggested using Yoder V Wisconsin as precedent, I would suggest to think very strongly about it. I don’t think the Satmar or many of the Chassidic Yeshivas would win using such arguments. One of the key points in that case was that the Amish refused social programs and engaged in further vocational training, which resulted in them not being a social burden. Towns like Kiryas Joel and New Square as 2 notable examples of the products of the Satmar and New Square schools, are both heavily dependent on social programs.
As to the non-Chassidic schools, if the State can show a relatively high dependency on social programs (which may be a real issue due to the numerous number of people in Kollel) they may also find that the religious opposition to secular education won’t fly. Once the burden on social programs is significant, the State will claim they have a vested interest, which allows them to burden religious practice.
One other point… For all those supporting the Trump/Conservative bandwagon, just remember that the conservative justices are more likely to take a dim view to relying on social programs. I would actually suspect on this issue, you would find both the liberal and conservative justices finding for the State and against the Yeshivas.