There are a variety of ways to address the privacy issues. One is to have the school as your customer only, and require it to manage the sub-accounts for students. In this way, you do not collect any personal information from the students since they are not your customer. The school is the administrator of the accounts and functions as a trustee of the funds.
This also avoids the issue of having minor accounts.
You would want to ask those banks that are operating these in school banks how they handle privacy when students are acting as tellers and customer service reps.
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Societies that do not find work in and of itself "pleasing to God and requisite to Man," tend to be highly corrupt.