The schools' officials have accused the government of discrimination, pointing out that in May, Netanyahu agreed to cover in full the budget of two networks of independent schools for ultra-Orthodox Jews, in return for their parties joining his coalition.
Many of the church schools have a matriculation rate of 95 percent, better than most of Israel's top Jewish schools.
Yet, with Palestinian families three-and-a-half times more likely to be below the poverty line than Jewish families, parents are already struggling to pay existing fees, according to the schools.
The alternative for these families is to take their children to state-run Arab schools, where the dropout rate is 17 percent, and barely more than a quarter of students matriculate.
Nabila Espanioly, director of the Tafula child development centre in Nazareth, said the poor performance of Arab state schools could be explained by decades of severe discrimination.
Studies by the Follow-Up Committee for Arab Education show that Jewish pupils receive at least five times more funding than Arab pupils -- $1,100 each compared to $192.
The Arab sector suffers from a shortage of more than 6,000 classrooms and 4,000 teachers.
Jewish schools have twice as many computers relative to their student body than Arab schools.
In addition, Palestinian leaders have long complained of interference by the Shin Bet, Israel's internal security agency, in the appointment and promotion of teachers in the Arab state system, undermining educational values and the professionalism of its staff.
"Parents want quality education for their children but the reality is that the only good choice for most of them is one of these church schools," Espanioly said.
Many of the community's leaders -- academics, professionals, and Knesset members -- were educated in such schools, observed Oudeh Bisharat in a recent column for the Haaretz daily.
Israel now appeared "determined to crush" the system because of its very success, he added.
Boutros Mansour, principal of the Baptist school in Nazareth, said the church-run schools expected the same treatment as the large number of independent schools for some 200,000 Jewish children from the religious ultra-Orthodox community, known as Haredim. They are fully funded by the government.
"The ridiculous thing is that the schools for the Haredim break the law by refusing to teach the core curriculum, including subjects like math, English and science, and they get 100 percent funding," he said.
"We, on the other hand, teach more than the core curriculum and have some of the best results in the country, and yet we are being starved of funds and are in danger of closure," he added.
The education ministry was unavailable for comment. But in a statement last month to Haaretz, it said the church schools had rejected all of its proposals.