Being exempt for withholding purposes is not the same as being exempt from income and SE-tax liabilities.  The only exclusion that applies to ministers would be allowances designated as parsonage, which is limited by §107 to:

1. the rental value of the home furnished as part of his compensation; or
2. the rental allowance paid to him as part of his compensation, to the extent used by him to rent or provide a home and to the extent such allowance does not exceed the fair rental value of the home, including furnishings and appurtenances such as a garage, plus the cost of utilities.

The Code does not extend any preferential tax treatment to religious ministers per se but rationalizes this exclusion as being akin to §119.

CA does not conform to subsection (2) in limiting the exclusion to the fair rental value of the home pursuant to RTC §17131.6.

This exclusion also does not apply to SE-tax (unless exemption is granted by the IRS).  In the absence of income tax withholding, the minister would also be required to make quarterly ES-tax payments or could otherwise be subject to underpayment of ES-tax penalty.