For Medicaid you only have to report what you declare on your tax return.
For snap your supposed to declare any money you get whether you declare it on your return or not.
Source
See the
SNAP sourcebook* section 13 for allowable exclusions from SNAP income. There's no allowable exclusion for parsonage income.
Under the old Medicaid regulations there was no allowed exclusion for parsonage income. Under the new regulations the MAGI calculation incorporates a substantial amount of tax law, and I'm not certain whether the parsonage exclusion was imported. My assumption is that it would not be, since you must pay self-employment tax on parsonage.
*The linked sourcebook is NY-focused, but SNAP regulations are federally-controlled and there shouldn't be significant differences by state.
ETA: Further research indicates that MAGI does not include clergy housing allowances.