When the Obama administration made the decision to require Catholic-run organizations to pay for health-care plans that include contraception, officials no doubt expected its critics to attack. What they didn’t expect, I’m just as certain, is that those friendly to so many of its policies would cry foul, too.

It’s an issue that won’t go away and the White House knows it. The DNC rapid response team is hard at work, issuing releases that explain how the rules won’t apply to churches and pointing out that many Catholic universities and hospitals already cover contraception in their plans.

Democrats are sharing survey results that say nearly six in 10 Catholics agree that employers should provide health plans that cover birth control at no cost. Fellow Republican Newt Gingrich is attacking what he says are Mitt Romney’s own inconsistency on the issue when he was governor of Massachusetts.

All those things are true, and they are also beside the point. It’s more emotional than logical, this feeling among many religious Americans, Catholics in particular, that the separation of church and state is not protecting the church as it should. Are there contradictions among word and deed?

Sure: You don’t see the big families in the pews that were routine in the past. (The five kids in my Catholic household fit right in at St. Pius V). But that doesn’t mean Catholics don’t aspire to be faithful and don’t respect the rules, even those they break.

It’s a mistake that politicians and parties make, categorizing Americans into red vs. blue, poor vs. hard-working middle class, godless secularists vs. true believers. They don’t get that most people are both-and, not either-or. As someone in that small Venn diagram overlap of African American and Catholic, I can attest that issues and people are more complicated than any survey could ever show.

There are many Catholics angry with bishops and clergy more concerned with male hierarchy and harsh directives than tending the flock. But they return to Mass each Sunday for a renewal of faith and strength to face the week ahead. Liberal and progressive Catholics reject punitive rhetoric, and admire the church most for the way it reaches out to all — regardless of denomination or station — in schools and hospitals.

Many supported affordable health-care legislation because it fits that mission, and they feel that those in the trenches, doing good work with little reward, will have to make tough choices between serving those in need and being true to their beliefs.

Just like in life, you criticize your own family members but circle around when they feel threatened in any way. These supporters of health care for all weren’t looking for a capitulation, just a compromise from an administration that has given Catholic organizations financial and moral support in the past.

One of them is my colleague Melinda Henneberger, who questioned administration actions and at the same time said the church does itself no favors when a bishop uses his power to kick out a priest for praying wrong. She noted that Obama “has handed his critics an example of an action that fits nicely with the narrative that he’s a secularist who looks down on believers,” something the administration never intended.

Of course Republicans candidates have jumped on this latest controversy — throwing in a measure of distortion and exaggeration — sensing an opening on the social issue front now that the economy is nudging up. It’s politics.

David Axelrod had to step up, defending the position of the Health and Human Services Department at the same time he hints at a compromise and emphasizes the year-long delay in implementation.

You can understand why the administration made too many assumptions about how people might interpret freedom of expression in a free society. And you can feel conflicted about the reach of religion, even your own, and still want government to give it the benefit of the doubt.

Mary C. Curtis, an award-winning multimedia journalist in Charlotte, N.C., is a contributor to The Root, Fox News Charlotte, NPR and Nieman Watchdog blog. She has worked at The New York Times, Charlotte Observer and as national correspondent for Politics Daily. Follow her on Twitter: @mcurtisnc3.