Actually, I thought Medishare and Liberty were non Christian but they are not. Here is a link to one that isn't Christian base but they want you to "believe in a god of some sort". It looks like that might be the only one.
https://www.healthforcalifornia.com/health-share-plans/aliera-health-care/aca-alternative
https://www.healthforcalifornia.com/health-share-plans/aliera-health-care/aca-alternative