There is no good reason for churches to be tax exempt, except that:

Churches are generally not-for-profit. As far as taxes are laid upon "income", it's hard to find taxable income amongst not-for-profit enterprises. As long a the government sees fit to "exempt" not-for-profit enterprises from taxes, it would be hard to not exempt churches in the mix, which is also a part of:

Taxing churches could be seen as "respecting an establishment of religion". There is no good way to tax churches that wouldn't be seen as favoring some churches over others, or potentially discouraging attendance, or otherwise punitive against some or all churches. There have been court cases to this effect.

The idea that tax-exempt churches shouldn't engage in political speech is flimsy. However, under the Internal Revenue Code, exempt organizations under 501(c)(3) cannot participate in various "campaign" activities, which has been interpreted broadly by the IRS and the courts, but only enforced rarely and selectively. This is ostensibly to prevent charitable and religious organizations from being used as fronts for laundering taxable political donations and/or contributions as tax exempt (for both the donor, and/or the receiving organization).