The question is not whether churches should be taxed.
It is quite firmly established and generally accepted (in the US) that non-profit organizations, and particularly those that provide a public benefit, may be, and should be, exempted from taxes.
The majority of non-profits comply with the requirements that they periodically demonstrate, by filing appropriate statements with the various tax jurisdictions, that they are in fact not for profit. The majority of non-profits are subject to taxes on profit making ventures, to the extent that profits go to the benefit of the organization and not to the provision of the "good works" that the organization performs. (This conforms to the requirement that individuals pay taxes on income that is to their own benefit.)
Churches, and to large extent anyone claiming to be religious-based, have been exempted from demonstrating that they are, and remain, non-profit, largely through the REFUSAL of the IRS to require such organizations to certify their non-profit status, even in cases where there is substantial evidence that the organizations have other than benefit to society at their core of purpose.
The government in the US CANNOT exempt churches from taxation on the basis of their being churches. It can and does exempt them from many taxes on the same basis that it exempts other non-profit, and in some cases "public benefit," organizations and agencies. It does have the authority to question the status of any agency or organization, with respect to exemption from taxation, provided that all such organizations are treated equally.
Churches are not, and have not been, treated on the same basis as other non-profit organizations.
No "exemption" from income taxes is required for a non-profit organization. If you have no income you pay no income taxes. Expenses of "doing your work" are reasonably allowable deductions from gross income in the determination of your "profit" or taxable income. A very broad interpretation of what is an "expense of the business" of saving souls probably is acceptable. The exemption from accounting for income and expenses is NOT ACCEPTABLE to many of us.
An exemption from payment of property taxes may not be given based solely on the property being "a church," but IF SIMILAR EXEMPTIONS are available to other agencies performing public services without profit from them, on the same basis, then there is no particular argument with exempting a non-profit organization from payment of property taxes.
The only need is to treat religious organizations the same as we treat non-religious ones. That DOES NOT IMPLY that the good works of the churches must be in any way restricted or curtailed - for tax purposes.