Even in churches without official tithes, there's a collection plate passed. Operations must be funded, employees need to be fed, housed, clothed.
That's also tithing (and is completely normal for regular church goers... bible says 10% to the church and a lot of folks follow that prescription)
Reality is, most non-profits' (church & non-church like NPR) budgets are funded by a small handful of very wealthy/generous donors. Not even 80%/20% rule, more like 80% of donations/sponsorships are from ~5% of the people giving money, the other 95% people giving's total is a small % of budget.
That's why in all non-profits, the leadership has to 'report' to a small number or rich donors. Piss off a couple of the rich, your non-profit will fold.