Under the opinion the 1st Amendment protection was NOT decided because the RFRA already protects religious exercise (acts motivated by religious conviction) - it says nothing about pieces of paper holding a system of religious belief. does it? It makes clear that what is protected is religious exercise by a legal "person" whether or not it is compelled by a system of religious belief.
But a corporation can't have beliefs. A corporation is a legal entity that exists only on paper. A corporation is shielded from certain liabilities and is also required to meet certain regulations. A corporation can not have religious affiliation as it is anthropomorphic.
Recall that an affiliation with a religion is irrelevant (see above). What I think you might mean, more accurately, is that a corporation cannot exercise religion because we are ascribing human characteristics to something that is not human. But whether or not you think a corporation should have the right to exercise religion due to the nature of its being, that is a separate issue from whether or not a corporation can "exercise", i.e. do a task, piece of work, activity, or process that can be characterized as religious. It may exercise religion BUT that does not mean it is protected.
Anyway, it ought to be self-evident that a corporation can do a task or activity that is religious in nature. Just as a corporation can have an exercise in public relations, advertising, or team building, it may have an exercise for religious purposes. An exercise is a task or activity or conduct with a specific purpose (such as making money), and unless you are willing to claim that corporations can't have any activities (excercises) with a purpose because it is not a human being you would be philosophically inconsistent without justification.
There are, of course, plenty of examples of corporations that exercise religion, some non-profit, others for profit. Religious book publishers, book stores, charities, foundations, and and trusts (for example). So yes, partnerships, LLCs, Trusts, Unions, and Corporations (profit and non-profit) can exercise religion.
THEREFORE, there is only one valid question left; "Does RFRA limit its protection ONLY to individual persons and if so, does that preclude the protection of all other forms of associations"?
The Religious Freedom Restoration Act of 1993 (RFRA) prohibits the “Government [from] substantially burden[ing] a person’s exercise of religion even if the burden results from a rule of general applicability” unless the Government “demonstrates that application of the burden to the person—(1) is in furtherance of a compelling governmental interest; and (2) is the least restrictive means of furthering that compelling governmental interest.” 42 U. S. C. §§2000bb–1(a), (b). As amended by the Religious Land Use and Institutionalized Persons Act of 2000 (RLUIPA), RFRA covers “any exercise of religion, whether or not compelled by, or central to, a system of religious belief.” §2000cc–5(7)(A).At issue here are regulations promulgated by the Department of Health and Human Services (HHS) under the Patient Protection and Affordable Care Act of 2010 (ACA), which, as relevant here, requires specified employers’ group health plans to furnish “preventive care and screenings” for women without “any cost sharing requirements,”42 U. S. C. §300gg–13(a)(4). Congress did not specify what types of preventive care must be covered; it authorized the Health Resources and Services Administration, a component of HHS, to decide. Ibid. Nonexempt employers are generally required to provide coverage for the 20 contraceptive methods approved by the Food and Drug Admin
Here is the rub, what exactly is restrictive about a health care provider providing a service? Health care provider gives the birth control to the patient. The insurance provider subsequently reimburses for the birth control. At what point is the privately held corporation involved at all in that process?
When the private employer is mandated to obtain an ACA approved policy that supports a certain kind of birth control, then the private employer is involved in the process because he, not the employee, signs the group policy contract.