need to figure out what's making the IRS uncomfortable

If we can identify a concrete concern that the IRS has about the funding of these organisations versus what they do we can perhaps find a formula that addresses that concern.

For example, the UK has a non-governmental body that sanctions advertisers whose creations are misleading, or distasteful called the ASA. Since it's not funded by the taxpayer it gets money from (some subset of) the advertisers it is regulating. A naive funding mechanic would make it easy for a big company to effectively "pay off" the watchdog. But instead the watchdog and the funding are kept at arm's length, any particular company that runs adverts might or might not be funding the ASA, the ASA doesn't know, its oversight applies regardless.