Hobby Lobby, the arts-and-crafts giant who challenged Obamacare’s mandate to provide coverage for all forms of contraception, won at the Supreme Court yesterday in a 5-4 vote. No surprise: The five justices on the majority side were all male, and the Court’s three women justices (along with Justice Breyer) sided with the government.

Too many reports and comments today have included this fact as though it is only to be expected that women would favor the birth-control mandate, which has been portrayed as central for women’s health.  Any opposition to it, sadly, has been and will be demagouged as a “war on women.”

But the truth is that Justices Ruth Bader Ginsburg, Elena Kagan, and Sonia Sotomayor are driven by a big-government ideology, not their sex. Women in the United States have diverse views on the size and role of government — including whether government should force religious employers to cover contraception for their employees. The media shouldn’t assume that this sample of three women represents us all.

Gallup polling from 2009 shows 37 percent of women identify as conservative, while 23 percent say they are liberal. This is a smaller margin than for men (44 percent vs. 20 percent), but still serves to show that not all women see the world like the female justices, who were all appointed by Democrats (two by President Obama).

Abortion is a divisive issue too: Although it is sometimes depicted as a women’s issue or even a women’s right, American women are divided on the issue. According to Gallup, 47 percent of women self-identify as pro-choice and 46 percent say they are pro-life.

Planned Parenthood and other pro-government organizations conducted polling specifically on the Hobby Lobby case and found that 68 percent of women disagreed with the arts-and-crafts retailer. This was no surprise given the degree to which the case has been misrepresented by left-leaning women’s organizations and abortion groups.

The National Organization for Women mischaracterized the intention of those challening the mandate as “bigotry toward women” and an attempt to “block women’s access to safe and effective contraception.”  If that were what the case was truly about, then naturally many women would be upset. A strong majority says birth control is morally acceptable.

However, the Hobby Lobby case had little to do with abortion, or even birth control. This was a case about government coercion.

Let’s keep in mind who was doing the coercing here: Hobby Lobby is not attempting to block women from using the contraceptive methods of their choice, from participating in other activities that the owners find morally objectionable, or even from seeking an abortion. They aren’t attempting to regulate women’s behavior — they have absolutely no ability to do so. Hobby Lobby simply refused to use company resources to fund coverage for certain drugs. It’s the government who was attempting to coerce the business owners to act against their will.

Notably, even according to Planned Parenthood’s polling data, nearly one third of women have seen through the hazy misinformation and side with Hobby Lobby.  In other polling data (not gender specific), 59 percent of likely voters oppose the mandate.

There are many religious, pro-life, and conservative women’s organizations that filed amicus briefs arguing against the contraceptive mandate, and many of their protesters were present at the Supreme Court this morning.

Ironically, the pro-government protesters carried signs that said, “Birth control: Not my boss’s business.” This slogan is enough to inspire support for Hobby Lobby, who was asking to not be party to women’s decision to use emergency contraception.

There are also women who sided with Hobby Lobby, not because they share the company’s convictions on Christianity, birth control, or abortion, but simply because we recognize that in America, no one should be forced to violate his or her religious conscience to pay for someone else’s choices. That’s the case with Independent Women’s Forum’s amicus brief.

Some SCOTUS watchers believed that the women of the Court sided with the government because they are empathetic to the women who work for Hobby Lobby.  But of course, it’s possible to empathize with women who are facing financial stress over their birth-control costs without condoning the contraception mandate.

As the majority wrote in their opinion, there are less-freedom-restricting policies that Congress could have enacted that would have assisted these female workers — like a tax-credit for birth control expenses or a public-health program funded by taxes — without burdening the employer. This is significant because the legal hurdle the government failed to satisfy was to show that no alternative, less-freedom-restrictive policies could have helped the government reach its goal.

The media will likely continue to parrot the idea that the real issue at stake in this case is women’s health, and it’s only natural that the women justices sided with the government.  But millions of American women who value the freedom of conscience and truly want their employers out of their birth control decisions know otherwise. We know that Burwell v. Hobby Lobby was about the limits of government’s power — and that’s a principle that all women (and men) should be glad to see the Supreme Court uphold.

— Hadley Heath is a senior policy analyst at the Independent Women’s Forum.