When we talk about the Catholic Church, we are usually referring to the Catholic religion, not a specific church. When we talk about freedom of religion, and the Free Exercise Clause in the Constitution, we mean the freedom to practice whatever faith we wish, or no faith at all.
A church is not a religion. A church is a place where you can go to (get sales pitches) learn about and practice your religion. But you can also study and practice it at home…or anywhere else, as long as that practice does not break any laws.
A church is a business in every sense. It has income, a budget, operating expenses, a staff of paid workers, and a facility where the business is done. What is a church’s business? Selling ideas, mainly. That’s what the media do too. It’s really no different. Why should a church be treated any differently from any other business? Why should churches get special privileges like income and property tax exemptions, immunity from IRS audits, tax deductions for donors, etc.? That has nothing to do with “free exercise.” If they do charity work, then that part of their business should be treated like any other secular charity. But it is not. Secular charities are subject to IRS audit. Churches are not. Churches are treated as non-profit businesses, but the IRS does not have any idea how much money a church takes in, or what they do with it. Charitable activities are usually a small part of a church’s budget.
It is a huge stretch of the Free Exercise Clause to grant these special privileges to businesses that sell religion. Why isn’t it a violation of the Establishment Clause, which not only forbids the government from establishing an official religion, but also prohibits government actions that unduly favor one religion over another. It also prohibits the government from unduly preferring religion over non-religion, or non-religion over religion. https://www.law.cornell.edu/wex/establishment_clause
How can it possibly be argued that all of the special privileges granted to churches are not unduly preferring religion over non-religion?
Here is a discussion of the pros and cons of tax exemption for churches. For me, the list of cons is far more convincing. Your mileage may differ.