I believe that any group that currently is exempted from social security would also be exempt from Obamacare. That includes Mennonites and Scientologists.
I found the full requirements:
Members of certain religious groups may qualify for an exemption from the Social Security tax. To do so, they must:
* Waive their rights to all benefits under the Social Security Act, including hospital insurance benefits; and
* Meet the following requirements:
1. Be a member of a recognized religious sect conscientiously opposed to accepting benefits;.
2. Be a member of a religious sect that makes a reasonable provision for its dependent members and has done so continuously since December 31, 1950.
3. Have never received or been entitled to any benefits payable under Social Security programs;
If you meet all these stipulations you can claim the Social Security self-employment tax exemption. To do so, file IRS Form 4029 (Application for Exemption From Social Security and Medicare Taxes and Waiver of Benefits) with the Social Security Administration.