Not true. There are different classes of nonprofit and they are not all tax deductible. Some nonprofits opt to forgo pursuing that status because it involves a lot of extra administration/filing requirements.
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.