There's often a crucial difference in the nature of "revenue": With nonprofits it's often a voluntary contribution ("donation"). Or non profits can rightly claim that the contribution is of a capital nature in which case it's equivalent to an equity raise for a business (share issue even though the shares will never pay dividends).
Donations and equity raises are not taxable income.
Many large non-profits actually make most of their money as returns from investments. The Mormon church is not at all unusual in this way - most large universities also make most of their money from investments. As an example, when I reviewed the Universty of Texas finances in 2019 I think it was, they could have charged zero tuition for every student across every campus and still would have had a positive net income for the year. Massive endowments are useful for this exact purpose - allowing operations even without any outside contributions.
You're probably thinking of one type of nonprofit but there are several. The church in this case is operate for any more like a non-profit Hospital or business. You can run Starbucks or Apple as a non-profit. As long as you don't return profit to the individual owners and keep it in the business, you can qualify
The Guardian newspaper in the UK is owned by a non-profit (Scott Trust). Its founder was concerned that his family would lose control of the newspaper after his death, being forced to sell a large chunk of it in order to pay estate taxes. So he set up a trust, more recently converted to a not-for-profit company, to control it. The company’s constitution says it cannot pay dividends, that its stock has no voting rights and cannot be transferred without the board’s consent, and that it cannot be acquired by any for-profit entity. The board is self-perpetuating, appointing its own future members. I believe the board members are issued stock upon joining the board, but are legally required to return it upon leaving. The actual media business is run by a 100% owned for-profit subsidiary. There’s no reason in principle why a business in any other industry could not adopt the same ownership model, although it does make it harder to raise capital.
> There’s no reason in principle why a business in any other industry could not adopt the same ownership model, although it does make it harder to raise capital.
Yes, it would make attracting capital harder. It would also make it implausible to ever consider leaving that business and doing something else if you're one of the owners.
Donations and equity raises are not taxable income.