As noted in the title, this is just the beginning of a thought, but I think there may be something about the public/private distinction at play in the recent (deplorable) “religious liberty” cases involving businesses. The question, it seems to me, is whether a business is public or private. The vague Hobby Lobby standard of “small, closely-held companies” seems to indicate that there are certain types of businesses that are more like a private concern, and hence you have control over whether your values are respected in that space. The implicit contrast is with publicly-held companies, which are (in principle) owned by “the public at large” and hence can’t demand the same kinds of rights that businesses more associated with a defined individual or group can.
In Aristotle, the economic realm is what we would call private. It’s something like the threshold of the political — there are forms of power at work, it is necessary as a support of the political, but it’s not yet the political. The modern concept of economy seems to carry the economic at least partway across the threshold, insofar as the economic is the realm of contract and law, etc. Yet in the terms of classical liberal political theory, there’s also a sense in which it remains a pre-political space, a presupposed background to political deliberation.
A “publicly held” company is fully across the threshold — it has entered into the public realm and is accountable to public norms. The “privately held” company is part of an individual’s property, conceptually a part of his “household” — and here I’m thinking in the full Aristotelian sense, where the workers he hires are also included in his household, as were the household slaves for Aristotle. It may be creepy and weird (not to say illegal) for the HR director at Bank of America to take an interest in the sexual practices of employees, but what about for a servant I’m inviting into my home? Perhaps it makes sense that this is the new staging ground for the “family values” campaigns of the conservative movement.