However, there's a major sense in which this is entirely about contraception ... a sense which is inherent in both The Freeman post and in the Catholic Church's stance on this issue.
You see, the author discusses a claim (from a Catholic) that there were "legitimate liberty interests on both sides of this debate." His argument is that the only claim with any legitimacy is the religious liberty claim. The claim that women have the right to contraception is, in his argument, fundamentally invalid.
But that's precisely the point that's in question. If contraception access (for free) is a fundamental right, then there are conflicting liberty interests.
Religious Liberty Limitations
As far as I know, no one is actually questioning whether religion has a fundamental liberty interest. No one is saying that religious liberty shouldn't be protected from intrusion by the government. The only question is whether the claim to contraceptive rights is valid.
However, we all recognize limitations on where religious liberty extends. There are fundamentalist Muslims who believe it's a moral right to pour battery acid on children who disobey their moral code. Virtually no one in America--not even the most ardent religious libertarian--would really argue that they should be allowed to do this. In fact, the government has a legitimate liberty interest to move in and intercede in these situations. Any law that prohibits battery acid assault restricts our hypothetical fundamentalist Muslim's "free exercise" of their religion.
So we all recognize that the government does have a right to intervene in ways that violate the letter of the First Amendment. The current issue is a debate where, from the President's perspective, he's trying to balance the two liberty interests (broad access to health care and religious rights of conscience).
The Freeman article makes a compelling case that these two claims are not equivalent, saying that health care is not a fundamental right. However, there is an organization which would disagree with that ... the Catholic Church.
Health Care as a Right
As if the situation weren't muddled enough already, there's the fact that, on the whole, the Catholic Church has been a major supporter of the Obamacare legislation from the beginning, according to not only George Will and Rick Santorum, but also stemming from their very own statement on the issue which begins:
Catholic teaching insists that health care is a basic right flowing from the sanctity of human life and dignity of the human person.
The Catholic statement goes on to protest wording in the legislation that may support abortions.
Still, the core is this: Catholic teachings indicate that "health care is a basic right." So health care would be a competing liberty interest, based specifically upon Catholic teachings.
Of course, Catholic teachings don't concede that birth control is a legitimate component of health care ... but it also doesn't agree with the greater thesis of The Freeman article (or the conservative attack on Obamacare) that mandating health care access is fundamentally a violation of individual liberty. In other words, they agree with the basic principle of Obamacare, but disagree with the specifics of the implementation.
So the first step in the debate is whether or not the health care legislation (and contraceptive access specifically) is constitutionally valid. That's a question for the Supreme Court ... and it is heading there shortly.
This specific religious liberty conflict is just one component of the greater debate over the role of the federal government in providing health care. The ultimate question is not about religious liberty, but about whether or not the government can mandate health care guidelines and force any institution to pay for them.
Once that is decided, then (if Obamacare is upheld) the question gets into a more detailed one of just and constitutional implementation ... and whether these competing liberty claims have equal standing.