For the most part, they are tax-privledged special interest groups. They really don't need any special "help" in the world. Unfortunately, this system has been "hacked" by tax and wealth management professionals. The examples range from the NFL to MOMA to Ivy League Universities, each harboring $10's of billions of capital, that is used to pay and protect already incredibly wealthy patrons and their benefactors.
As such, using their tax-exemption as a form of marketing is highly suspect. And, lets face it, this is the purpose of self-identification. The terms "non-profit" for example is merely calculated to express empathy; it fails to highlight "tax-dodge" or "income & asset laundering".
The notion that "non-profit" entities run $30Bn hedge funds and pay executive salaries in the multiple millions of $USD, all while being granted tax and regulatory exemptions, is something to think about.
DNS + simple hosting + support, is an ideal market for a non-profit focused on free speech and democratic participation.
I care how it handles my domains, policy and all that jazz, particularly in cases of hacks, take downs, etc...
I care about customer service.
I care about some options it offers that is and can genuinely be useful.
I care about what it does right or wrong.
Basically things that affect me and my domains/businesses.