This is a summary of the requirements for tax exempt status as a 501(c)(3):
"...it may not be an action organization, i.e., it may not attempt to influence legislation as a substantial part of its activities and it may not participate in any campaign activity for or against political candidates...
The organization must not be organized or operated for the benefit of private interests, and no part of a section 501(c)(3) organization's net earnings may inure to the benefit of any private shareholder or individual.
Section 501(c)(3) organizations are restricted in how much political and legislative (lobbying) activities they may conduct."
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Rather than just auditing organizations that are thought to be in violation, please require these groups to make their records public information.