That's a common internet myth, but no. (There is a religious exception to Obamacare, but it is defined as only those religions which are exempt from Social Security. I believe the only religions that have ever qualified are the Mennonites and the Old Order Amish-- religions which provide comprehensive care for all their members and refuse all government aid.)
It was a while back. The way it was usually stated was that since Muslim charities only cater to Muslims, they would be exempted. Since Christians charities cater to anyone, they would not be.