Setting more appropriate land taxes would be a good start, which is much easier then trying to figure out how to tax income. The harder part is reducing the tax liability based on the "public good" or "how benevolent" the organization is. Hard but not impossible. For example, a private golf club would pay higher taxes than a public golf course. Or a church that allows anyone in or has tons of community outreach to the neighborhood pays less or no taxes vs a church that has tons of requirements or hoops to jump through.
Churches in Europe are one of the biggest benefactors of tax free income, and also one of the biggest landowners in a lot of cities.
After the collapse of the Soviet Union, my country chose not to give back land taken from religious organisations - as they would end up giving more than half the city center to the Catholic church.
Plus to be considered legally a "religious organisation" often has many hoops and strict criteria to go through (at least here in Europe). Due to migration there are many small religious groups, but they aren't officially classed as a "religion" so cannot use the same tax breaks. Existing churches have a strong moat.
According to Glassdoor, the average salary for a Catholic priest in the United States in 2024 is $104,699 per year, with an estimated total pay of $206,187 per year. This includes an estimated additional pay of $101,488 per year, which could include cash bonuses, tips, commission, and profit sharing.
Priests are taxed as individuals so this doesn't seem relevant. But besides the fact that glassdoor's salary estimates are at best ludicrously off. Several of the top companies for "Catholic priest" on that page are protestant organizations, so I will take this with a grain of salt.
I don't think that figure is accurate. Most priests make under 100K. And priests are taxed as individuals, not as non profits, so I am not sure of the relevancy.