Families who have joined the groups recount winding up with medical bills not covered by the ministries, with no legal way to appeal decisions to reject coverage for care. Some groups ask their members to push hospitals and doctors to write off their bills rather than use members’ money to pay their expenses.

“These plans offer a false sense of security,” said Jenny Chumbley Hogue, who runs an insurance agency in the north Dallas area of Texas. She refuses to offer them to her clients.

Several states have taken action against one ministry they say has deceived people about what they are buying. “The nature of what we’re hearing from consumers around the state is absolutely heart breaking,” said Kate Harris, chief deputy insurance commissioner in Colorado, one state that is trying to prevent the ministry from operating there.

But health-share ministries have become particularly attractive to people like the Collie family who don’t qualify for a federal subsidy and can’t afford an A.C.A. plan. Even though premiums in the A.C.A. market have stabilized, critics of the law insist people need alternatives. “That’s the real driver behind the growth,” said Dr. Dave Weldon, a former Republican congressman from Florida who is president of the Alliance of Health Care Sharing Ministries, which represents the two largest groups.

When Dan Plato left his job to become self-employed as a consultant, he discovered that an A.C.A. policy for 2018 would cost his family around $1,300 a month. “It was very expensive and beyond our needs,” he said. Membership in Liberty Healthshare, a ministry established by Mennonites in Canton, Ohio, was less than half the price, according to Mr. Plato, who blogged about his experience.

But some Liberty members reported trouble getting their medical bills covered. Mr. Plato says a small bill for flu shots went unpaid and ended up in collection. At the end of the year, he was left wondering if Liberty would be able to cover the family in the event of a serious medical emergency. “It’s not something we could trust in that situation,” said Mr. Plato, who switched to one of the plans offered by United Healthcare also exempt from the A.C.A. rules for 2019.

Robyn Lytle, who works as an event planner in Chicago, joined Liberty for 2018, only to find that her daughter’s medical tests were never paid. “It’s been a year and a half, and I’ve been sent to collection,” said Ms. Lytle, who says Liberty had covered some of her family’s other expenses. She switched to an A.C.A. plan for 2019.