When it comes to donations, the IRS has clearly defined guidelines on what qualifies a donation to be tax deductible. See https://www.irs.gov/taxtopics/tc506 If the organization is not on the list, that doesn't mean they are not qualified. But to be sure the donor should ask the recipient organization for a copy of the letter they received from the IRS, approving them as such.
The only organization I"m aware of that will not be on the list or have a letter, will be religious organizations; such as a church for example. All churches are 50% organizations provided that church or religious organization is listed as such in the state or local property tax records. Generally (though not always) churches don't pay property taxes. Some churches are even registered with the state (as well as the IRS) as a tax-exempt 501c(3) organization, so be careful there. While a 501(c)3 may be exempt from paying taxes, that does not necessarily make them a qualified charitable organization. Finally, be aware that the tax treatment for a registered non-profit is not the same as it is for a registered not-for-profit.
Also keep in mind that there are two basic types of qualified charitable organizations one can donate to. For organizations classified as a 30% organization, only 30% of what is donated is tax deductible. For organizations classified as a 50% organization, only 50% of the donation is tax deductible.
