It’s not just income tax. Non-profits also don’t pay property taxes on the land and buildings they own.
On Boston, for example, around 30% of all property value is held by non-profits. This creates serious burdens on other taxpayers. And every time BU or BC or Harvard or Mass General buys up another building in the surrounding neighborhoods, it comes off the tax rolls and everybody else is left to make it up. It’s absurd that BU, for example, which owns $2 billion in real estate, does not have to pay a penny for the services provided by the city. (They do pay a small amount as a Payment In Lieu Of Taxes (PILOT) but the amount is not even close to what they’d pay if their property was taxed).
This isn’t a public vs. private issue though. In MA at least, state-owned property is not liable for local property tax, so the publics are just as bad as the privates in this case.