To wit, non-profit doesn't mean "doesn't take in money." IIRC, it means that the organization doesn't distribute surplus income (profit) to shareholders.
So, a non-profit that took monies from EU citizens I think would still possibly be affected, unless there's EU laws that make non-profits a different class of business subject do different laws.
There are non-profits that make millions of dollars in positive cash flow. All that term means (At least in the US) is that it doesn't ever pay dividends to shareholders.
I'll be intentionally vague because I don't want to stray too far afield but there are some large organization that make a lot of money but are classified as non-profit. They can pay excess revenue as bonuses to directors and executives.
Note that I said "de facto", not "de jure". Nobody would bother suing a non profit that doesn't have EU offices unless you were very large and/or very prominent and/or doing something really nefarious about the data you have. And even then, suing an US company with no EU standing in front of an EU court from an EU citizen complaint is far from easy.
The same reason that if, say, Texas introduce a law that says everyone commenting on a texan website needs to be polite and I post a comment with some name calling, suing me as someone not from Texas nor the US would not be very doable, even though I technically infringe on that law.
