Though at first glance the two things may seem utterly unrelated, there’s something oddly fitting about the fact that Pope Francis accepted the resignation of the controversial bishop of Limburg, Germany, just 24 hours before his much-anticipated first meeting with President Barack Obama of the United States.

Bishop Franz-Peter Tebartz-van Elst became infamous last fall as the “bling bishop” who spent more than $40 million remodeling his own residence. When Francis ousted him in October it was a shot heard round the Catholic world, signifying that the new pope’s call for a “poor church for the poor” was more than mere rhetoric. Today’s formal denouement to the Limburg saga cements that impression.

The impression of a grand alliance on behalf of the world’s poor is, of course, very much at the heart of what Obama would like to get out of tomorrow’s session – both as part of his eventual legacy, and with an eye towards the mid-term elections looming this fall.

It’s tempting to augur that Obama and Francis ought to be able to do business, since both are identified with what Christians call the “social gospel,” meaning concern for the poor and for peace. Obama, who began his career as a community organizer with a group founded with the support of some Chicago Catholic parishes, is a great admirer of the late Cardinal Joseph Bernardin of Chicago, who had a passion for the kind of Catholic social teaching enjoying a renaissance on Francis’ watch.

On the Vatican side, many officials in Rome always have been warmer to Obama than some American Catholic leaders. The editor of the Vatican newspaper, for example, declared in 2009 that Obama is not a “pro-abortion president.”

There’s also a concrete issue where the pope and the president share a political interest: Immigration reform. Obama has vowed that he wants to get something meaningful done for America’s millions of undocumented immigrants before the end of his presidency, ideally within the year. Francis devoted his political debut to a trip to the southern Mediterranean island of Lampedusa, a major point of arrival for impoverished migrants from Africa and the Middle East, to condemn a “globalization of indifference” to immigrants.

Later this month a delegation of American bishops, including Cardinal Sean P. O’Malley of Boston, will hold a series of events on the US/Mexico border intended to mimic the pope’s Lampedusa outing and to raise consciousness about the human toll of the immigration system. That’s both a humanitarian and a practical concern for a church in the United States whose membership is now one-third Hispanic.

Yet there are at least two key areas where Obama and Francis are not on the same page, suggesting that a deep partnership between the two leaders, akin to the anti-Communist “Holy Alliance” between the late Pope John Paul II and US President Ronald Reagan in the 1980s, may not be in the cards.

Life issues

Aside from the broad clash between Obama’s support for abortion rights and the Catholic church’s opposition, there’s also the specific matter of the contraception mandates imposed by the White House as part of health care reform. Sharp differences on that score still loom over the administration’s relationship with the church.

The US Supreme Court heard arguments yesterday in two cases arising from the requirement that private employers provide contraception as part of a basic health care package, and the legal and political fallout does not appear destined to end anytime soon.

Though Francis has indicated that he wants to dial down the rhetoric on life issues, there’s no indication of a substantive shift. Two days ago, in a message to members of a Vatican department that deals with health care issues, Francis again affirmed the importance of defending human life “from conception to natural death.”

In a Jan. 13 speech to diplomats, Francis called abortion a “horrific” crime, and he routinely lists the unborn among the victims of what he calls a “throw-away” culture.

Moreover, Francis is committed to what Catholics call collegiality, meaning decentralization of power away from Rome, one piece of which is respect for the decisions of local bishops. As a result, Francis likely will be reluctant to do anything perceived as undercutting the US bishops’ resentments over what many of them see as an erosion of religious freedom under Obama.

The Middle East

In broad strokes, both the Obama administration and the Vatican under Francis are in favor of improved relations with the Islamic world, both look with favor on the Arab Spring, and both support a resumption of peace talks between Israel and the Palestinians.

Yet at the level of detail, there are also differences.

On Egypt, Obama took a “pox on both your houses” stance last summer with regard to the Muslim Brotherhood and the army after a military council declared controversial President Mohamed Morsi deposed. The Vatican was more favorable to the military intervention, inclined to see it less as a coup and more as a reflection of popular will.

In Syria, the Obama administration has made the removal of President Bashar al-Assad a precondition for any negotiated end to that country’s civil war, while the Vatican is more skeptical about regime change, in part out of concern that whatever follows Assad might actually be worse.

Underlying these contrasts is that the Vatican’s reading of the Middle East is heavily conditioned by the perceptions of the Christian minorities in these countries, who generally see either a powerful military or strong-arm rulers as a buffer between themselves and Islamic radicalism. They often point to Iraq, where a once-thriving Christian community has been gutted in the chaos that followed the collapse of Saddam Hussein.

Few on the Catholic side are inclined to see the Obama administration as a great defender of those Christians at risk, while standing up against violent anti-Christian persecution is emerging as a cornerstone of Francis’ social and political agenda.

When tomorrow’s meeting wraps up, it’s likely that the statements issued by both sides will be friendly. As US Ambassador to the Vatican Ken Hackett said in a recent interview, “In this kind of high-level meeting, it’s not about making anybody feel bad.”

That said, it’s also not clear that a dramatic “reset” in church/state relations is likely either. It’s more plausible that the relationship will continue to be a complicated ballet, with each side looking to extract what it can get, driven more by strategic interests than any deeper spirit of common cause.