Amish, OK. Catholics, No.

[Warpy]

12. Although they don't call it insurance, what the Amish do is exactly that

Through the churches and community, they collect a pool of money to be used for members who get sick or whose barn burns down, whatever. It's still insurance. Since it's church based, the church dictates who the money goes to.

Had the RCC formed an insurance company, likely it would be exempt from insuring any woman between the navel and the knees, as befitting a patriarchal religious organization. It's hard to think of who would sign up for it, though, unless it was offered at a steep discount. Catholics are part of the world the Amish have pretty much rejected.