At least in the US, claiming that you are a nonprofit implies that contributions are tax deductible. Claiming that you are a nonprofit when contributions are not tax deductible might be considered fraudulent.
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.
I would love to see someone try to explain to the IRS why all those purchases of Amazon gift cards and Monero for the transparently illegal organization should be deductible though