A major problem is that many charitable organizations are sponsored by churches, and get their non-profit status and Tax ID EIN from the parent church.
For example,  parochial schools, food pantries, PAD shelters for the homeless,  etc.   If Google looks up the EIN Tax ID and sees it is a church, it may automatically reject many requests for no good reason.  I suspect that is what is happening to our Computer Refurbishing group, which gets its non-profit status from our church, but
our function is a charity, NOT a church.

I'm still not absolutely sure why we were rejected.  Getting pointed to a document that has over a dozen ways to get rejected is not constructive or helpful.  (Maybe they didn't like our not-yet-published web site?)

I also noted that many people are getting rejected because the EIN tax ID is "already in use or registered".  This is highly likely for organizations that have multiple charitable (non-profit) functions.   Why is this a problem?  Our web site and domain will be entirely different.  Do we have to sub-domain the parent organization's domain to get past this artificial limitation,  just to get around the shared EIN Tax ID?

-- A frustrated potential user of Google Apps for Non-Profits