A housing allowance provided to a minister as part of the minister’s pay generally is not subject to income tax but is included in net earnings from self-employment. For that reason, it is included in earned income for EITC, unless you have an approved Form 4361 or Form 4029.
For more info, see this article: https://www.irs.gov/credits-deductions/individuals/earned-income-tax-credit/special-eitc-rules
