You're responding to a different point than the one I made. It's true that being a "nonprofit" doesn't logically entail that donations will be tax decudtible. But it still implies it to potential donors. The former is a matter of logic, the latter is a matter of psychology. Both are relevant.

Yes, there are multiple classes of nonprofit, not all of which are tax deductible. But it is also true that holding yourself out to the public as a "nonprofit" has the potential to mislead because it may imply to potential donors that contributions would be tax deductible. That is why responsible (or at least well advised) nonprofits disclose which they are, because claiming you're a "nonprofit" in marketing materials, without further explanation, can mislead potential donors.