I am not aware of any reason that you would have to charge fees from parents to retain your tax-exempt status.  It is possible that there may be a payment requirement from the league of which you are a part but I am not familiar with such a requirement.  The IRS does not care whether you get fees from parents or gifts from others, so long as you get enough public support to be considered a public charity and not a private foundation.

Perhaps the more compelling reason to charge fees is that it would be hard to raise enough money through contributions to meet all of the costs of the organization.  In addition, when you talk about ad book sales, particularly if they are regularly carried on, you may be talking about generating unrelated business taxable income. Such income would not only be taxable, but if it is a substantial non-charitable activity, could cost your exempt status.  (See Ready Reference Page: “Charities Often Worry About UBIT”) 

It is a better practice to have a diversified source of funding to provide stability for your operation, using fundraising to provide scholarship type assistance to kids who can’t afford the basic fee.