Reader Luke H. has written in to point out that Mr. Ramsey has in fact discussed Christian healthcare sharing ministries, and Medi-Share specifically, on his site.
He then points out correctly that Christian health insurance alternatives are not insurance and don't face the same regulations as insurance companies. What this means is that you need one that has a long track record of serving their members, such as the 24 years that Medi-Share has been providing affordable healthcare sharing.
For more information, see Mr. Ramsey's post about it here. What is your favorite Dave Ramsey wisdom?