Don’t pick a fight, the saying goes, with a man who buys ink by the barrel. Here’s a corollary for President Obama: Don’t pick a fight with an elderly, retired, cloistered nun who founded the world’s largest religious media network.

That is precisely the mistake Obama made when his administration announced that religious employers like Mother Angelica’s Eternal Word Television Network (EWTN) would be forced to provide coverage for contraception, sterilization, and abortion-inducing drugs — a violation of their deeply held religious beliefs. The Obama policy, EWTN declared in a federal lawsuit last week, is “un-American, unprecedented and flagrantly unconstitutional.”

Millions of Americans agreed. And faced with a political firestorm, President Obama on Friday announced what he termed an “accommodation” of religious employers: the mandate to provide abortifacient drugs, sterilization and contraception would remain in place — but insurers will be required to provide them for “free.” The decision has been called everything from a compromise to capitulation — but in truth the president didn’t retreat one inch.

Under the revised policy Obama announced, the government still coerces religious institutions to purchase insurance policies that include services they consider gravely immoral. And put aside, for a moment, Obama’s arrogance in presuming that the federal government can simply order private businesses to give a product away for free. Liberals like Obama don’t seem to realize that there is nothing “free” in this world. Unlike many of the religious groups Obama has targeted, insurance companies are not charities. Someone will have to pay. That someone will eventually be the religious institutions. The costs will be passed on, over time, via higher premiums — which means religious employers will still be forced to pay for services they consider immoral and unjust.

Moreover, many religious employers (including EWTN) “self-insure.” This means the religious organization acts as its own insurance company — paying for care directly and using insurers only to manage benefits and process claims. Many religious organizations took this step so they could opt out of state mandates to provide morally-objectionable services. As a result, in the case of religious employers like EWTN, there is no insurance company to provide the “free” abortion drugs and contraceptives Obama has mandated.

Bottom line: The Obama “accommodation” is a sham — and a brilliant one at that. The president somehow managed to create the impression he backtracked on his decision and offered a reasonable compromise — without giving up any ground whatsoever.

Obama’s objective is to get this story off the front pages until after the election, and divide his opposition. He has succeeded to some extent. The Wall Street Journal headline Saturday blared (incorrectly): “Obama retreats on contraception.” And some on the Catholic left like Sister Carol Keehan, head of the U.S. Catholic Health Association, quickly grabbed the fig leaf Obama offered them.

But EWTN isn’t buying Obama’s ruse — and neither are the nation’s Catholic bishops. On Friday night, the U.S. Conference of Catholic Bishops issued a strong statement rejecting Obama’s false accommodation, declaring “The only complete solution to this religious liberty problem is for [the Department of Health and Human Services] to rescind the mandate of these objectionable services. We will therefore continue — with no less vigor, no less sense of urgency — our efforts to correct this problem through the other two branches of government.”

That is precisely what EWTN is doing. Hannah Smith, senior counsel for the Becket Fund for Religious Liberty which is representing EWTN, told me, “The president’s announcement changes nothing from a legal standpoint. He had a final rule that violates the Constitution and the Religious Freedom Restoration Act, so the Becket Fund is full steam ahead in our lawsuits challenging the mandate.” (Becket is also suing on behalf of Belmont Abbey College, a Benedictine Catholic college in North Carolina, and Colorado Christian University, a nondenominational Christian University in Colorado).

The Becket suit calls that the Obama administration is “coerc]ing] EWTN to violate its deeply-held religious beliefs under threat of heavy fines and penalties” by “forcing EWTN to fund, promote and assist others to acquire services which EWTN believes involve gravely immoral practices, including the destruction of innocent human life.” This means “EWTN cannot provide health care insurance covering artificial contraception, sterilization, or abortion, or related education and counseling, without violating its deeply held religious beliefs.”

That is not going to happen at a network founded by Mother Angelica. Mother has retired from public life — but her fighting spirit continues to animate the network she built from a monastery garage into a religious broadcasting empire that spreads the Gospel to over 123 million households worldwide. Smith says Friday’s announcement made clear that Obama “will not back down until he forces religious groups to bow down to the altar of government-mandated health care.” To this altar, EWTN will not bow. As the network’s president and CEO, Michael P. Warsaw, put it, “Maybe they missed the word ‘Eternal’ in the name. The mission of EWTN is not negotiable.”

To that, Mother Angelica would say: Amen.

Marc A. Thiessen, a visiting fellow with the American Enterprise Institute and former chief speechwriter to President George W. Bush, writes a weekly online column for The Post.