The answer is unclear, and you may want to speak to a tax professional who specializes in church and related issues.
Briefly, under current regulations, a health sharing ministry does not count as "insurance" and payments to HSMs are not deductible medical insurance premiums. The IRS proposed a rule in 2020 that would allow HSMs to be classified as "insurance" but they have not moved to finalize or implement the rule (possibly because the rule was promoted by the former president, not the current president).
https://www.irs.gov/newsroom/proposed-regulations-address-direct-primary-care-arrangements-and-healt...
https://www.federalregister.gov/documents/2020/06/10/2020-12213/certain-medical-care-arrangements
Therefore, if the HSM is not insurance, are reimbursements for medical care considered insurance payouts or not? That's complicated and I don't know the answer. I have an analogy that suggests an answer, but I am not an attorney.
If you buy disability insurance with after-tax dollars, any disability income paid after an accident is not taxable, because the money you used to pay the premiums was already taxed. However, if you pay for the insurance with pre-tax payroll deduction or your employer pays the premiums tax-free, the disability income is taxable, because you never paid tax on that money before.
By implication, since premiums to an HSM are not tax-deductible, the reimbursement might not follow the usual rules. Maybe you can deduct your medical expenses even though they were reimbursed, because you paid tax on the money you used to pay the premiums.
Or, if the HSM is not insurance, is it a gift from the HSM? And if it's a gift, then you can still deduct the expenses, because money is fungible and gifts are not taxable to you. If you paid for medical care, and you get a gift of money, there's no way to say that the exact gift dollars were used for expenses, rather than the gift dollars were used for groceries and you used you own money for the medical expenses (this is what "fungible" means, more or less.)
So I think the answer is unclear. You could take a chance, or be cautious and not deduct the expenses, or seek out professional assistance.
