You have some reading to do.

What is it being paid out of? Who is paying it out? Who paid into it?

https://pastorswallet.com/claiming-a-ministers-housing-allowance-in-retirement/

https://cs.thomsonreuters.com/ua/ut/cs_us_en/ius/proc/retired-minister-housing-allowance.htm

Highlights:

A retired minister may receive rent-free use of a home or a rental allowance in recognition of past services as a minister. The lesser of the designated allowance, the fair rental value of the home, or the actual expense of maintaining the home is excludable from income. The taxable amount of any retirement distribution is reduced by the amount of a designated housing allowance.

Contributions you make to a church retirement plan, usually a 403(b)(9), as a pastor are a part of your pastoral income. So, when you take them out in retirement they are still considered eligible pastoral income. Any pension your church or denomination pays you is something that you earned through your ministerial work and part of your compensation as well. Also, if you use part of your church pension to purchase a commercial annuity, those annuity payments generally qualify for the housing allowance as well, since they were bought with your ministerial income.

You cannot take a housing allowance from an IRA in retirement, even if you used your pastoral compensation to fund it. Neither can you claim a housing allowance from your Social Security benefits, even if you paid into the system as a pastor.

The housing allowance must be officially designated in advance by the employing church or other qualified organization. The IRS has ruled that the board of a national denominational pension fund is qualified to make a housing allowance designation for a pastor. They determined that the pension fund met the requirements of being an “employing church” and the fund trustees were acting on behalf of local churches. Revenue Ruling 63-156 also allows for an independent or nondenominational church to designate a housing allowance for their retired clergy.