I don't see any relevance to the question of whether the booster organization is 501(c)(3) or not. With or without that status, donations are not "income," and at most your "income" is going to be maybe interest earned on a bank account, if any. The main reason to be 501(c)(3) is so that donors can deduct their contributions on their tax returns, if they itemize. Not pertinent to the discussion here.
I don't think a prior criminal investigation is needed to get the IRS involved. Anyone getting tens of thousands in cash and not accounting for it, the IRS will be interested, and they couldn't care less about the politics of it. This may be your route to get away from all the seeming "home cookin'" of the locals.
Sounds to me like the school had a prior scandal and the principal and AD want to sweep this second black eye under the rug. That's bad enough, but now you have a legit question about whether what happens to your son is deserved, or whether it's retribution or some attempt by him trying at to show you he's still the man. The integrity of everything is now legitimately in question; it's not to be dismissed as your typical parental whining.
This should never have been permitted to go on for more than, say, 30 days. If I were in charge, everyone who has dragged feet on this would be disciplined. Coach fired and prosecuted, AD possibly fired or demoted, principal disciplined as well. The fact that this guy is still coaching is inexcusable. It's not like the world lacks for guys who want to run baseball programs and who can do so on the up and up. There's just no reason to keep this guy around. Even if it turns out that he's just horrible with financial controls and accounting -- the "pure heart and empty head" defense -- that's good enough reason why he shouldn't be in a position that requires him to handle all receipts and disbursements. Anyone in a supervisory position should be able to see that. Even if there was no theft, the situation is a breeding ground for theft, and at best, no one has any idea what costs what, whether moneys are being spent wisely or wasted, and what fees should be assessed to conduct a legit program.