The tax-exempt status of churches enables charity work
A central focus of churches is caring for the poor and marginalized. They also provide services for the community. A church tax would force these institutions to channel less money into providing these services. As a result, the poor and marginalized would suffer from a lack of these previously offered resources. There are many charitable organizations who largely rely upon donations from church, including the National Christian Foundation and Catholic Charities USA (which serves 10 million people every year through 2,500 different agencies). Taxes would seriously undermine the hard work that these organizations do and take away money money meant for charity work and donations. Through providing these services, churches earn their tax-exempt status by contributing to the common good.
It is difficult to see the inner workings of church's funds and how much of them go to charities and the "common good." Many huge churches across the world, especially those formed around televangelist personalities, make boatloads of money but do not contribute significantly to charity or their local communities. Charity and the "common good" could be seen as an excuse for these churches to exploit their patrons without answering to the government, their organizations funding nebulous purposes, either for their own pockets or the pockets of their wealthy constituents.
[P1] The charity work religious institutions do has significant positive effects. [P2] If they were to pay taxes, they would no longer be able to carry this work out. [P3] The charity work does more good than their paying taxes would do. [P4] Churches should be exempt from taxes.
Rejecting the premises
[Rejecting P2] Paying taxes does not automatically mean churches cannot give to charity and give back to their local communities. If they are a larger church with a lot of revenue, they could still contribute significantly while being taxed at a slightly higher rate than zero. [Rejecting P3] This is not necessarily true - taxes are guaranteed to go into projects like schools and infrastructure, while charity work is not guaranteed by churches. [Rejecting P4] Churches should not necessarily be exempt from taxes.