If someone talks about the legitimacy of public schools and is a member of the Church, I would thoughtfully have them consider what the Prophets have said about public programs:
"I am opposed to free education as much as I am opposed to taking property from one man and giving it to another who knows not how to take care of it… I do not believe in allowing my charities to go through the hands of robbers who pocket nine-tenths themselves and give one tenth to the poor… Would I encourage free schools by taxation? No!"
Brigham Young, Journal of Discourses, vol 18, p. 357 General Conference, 1877
“When you accept food stamps, you accept an unearned handout that other working people are paying for. You do not earn food stamps or welfare payments. Every individual who accepts an unearned government gratuity is just as morally culpable as the individual who takes a handout from taxpayers’ money to pay his heat, electricity, or rent. There is no difference in principle between them… The price you pay for “something for nothing” may be more than you can afford. Do not rationalize your acceptance of government gratuities by saying, ‘I am a contributing taxpayer too.’ By doing this you contribute to the problem which is leading this nation to financial insolvency.”
President Ezra Taft Benson, BYU speech, 1977
"Occasionally, we receive questions as to the propriety of Church members receiving government assistance instead of Church assistance. Let me restate what is a fundamental principle. Individuals, to the extent possible, should provide for their own needs. Where the individual is unable to care for himself, his family should assist. Where the family is not able to provide, the Church should render assistance, not the government. We accept the basic principle that “though the people support the government, the government should not support the people.”
Latter-day Saints should not receive unearned welfare assistance from local or national agencies. This includes food stamps. Priesthood and Relief Society leaders should urge members to accept the Church welfare program and earn through the program that which they need, even though they may receive less food and money. By doing so, members will be spiritually strengthened, and they will maintain their dignity and self-respect.
Last year in the United States alone over $98 billion was distributed in unearned government transfer payments and other aid to millions of men and women who most often did nothing for what they received. This character-weakening government dole is repeated in almost every nation of the world. We encourage Latter-day Saints everywhere to remain free of government assistance. Work for what you receive."
Ezra Taft Benson, April 1977