So there is a proposed constitutional amendment that would remove the Blaine language from the State Constitution. The Blaine language is found in Article 83 and provides that the State may not financially support religious schools:
Blaine Amendments were pushback against Catholic immigration in the latter half of the 19th century. Public schools, at that time, were teaching generic Protestantism, and Catholic immigrants (who were being taxed to inculcate Protestantism) wanted the government either to cease that practice or to also provide funding to Catholic schools. Blaine was an anti-Catholic Congressman who proposed an amendment to the United States Constitution in 1875 that would have prevented States from providing financial aid to religious schools (while leaving “public schools” inculcating Protestantism free to continue inculcating Protestantism).
While the amendment failed to pass the United States Senate a majority of States, including New Hampshire, subsequently adopted versions of the Blaine Amendment. New Hampshire adopted its Blaine Amendment in 1877.
The United States Supreme Court … in October, 2019 in a decision called Espinoza vs. Montana … effectively struck down State Blaine Amendments because they violate the Free Exercise of Religion clause of the First Amendment by discriminating on the basis of religion:
CACR 3, however, maintains incorrectly that New Hampshire can continue to disqualify private schools because they are religious:
The Voters’ Guide language implies that CURRENTLY the State may NOT financially support religious schools. This is incorrect. If the State provides financial support to private education … say for example, via an “Education Freedom Account” … it MUST include religious schools.