Faith Based Healthcare is not insurance. Rather than paying premiums toward a plan which covers your health, these ministries work as a community of pooled money where one can submit their health care expenses and receive compensation based on other member's giving toward those expenses.
Membership fees for faith based health care and health sharing ministries are not HSA eligible. In order to add money to a health savings account, you will need a qualifying HDHP Insurance Plan.
If you no longer have coverage from an HDHP and still have a balance in your HSA, you can still use the funds in your account toward HSA Eligible Expenses.