Legislation imposing similarly repressive sanctions on gays has been proposed in Uganda, Cameroon and Tanzania.
In Nigeria, the leader of the hierarchy fully supported that country's new law, which prompted a wave of violence against gays when it passed.
In a January letter on behalf of the Catholic hierarchy of Nigeria, Archbishop Ignatius Kaigama of Jos praised Nigerian President Goodluck Jonathan for his "courageous and wise decision" in signing the legislation. Kaigama said it would protect Nigeria "against the conspiracy of the developed world to make our country and continent, the dumping ground for the promotion of all immoral practices."
A few days later, however, a strongly worded editorial in the The Southern Cross, a newspaper run jointly by the bishops of South Africa, Botswana and Swaziland, took aim at the new law, calling on the Catholic Church in Africa "to stand with the powerless" and "sound the alarm at the advance throughout Africa of draconian legislation aimed at criminalizing homosexuals."
The editorial decried the "deep-seated sense of homophobia" in Africa and said the church had too often been "silent, in some cases even quietly complicit" in the face of the new anti-gay measures. It also noted that the Catechism of the Catholic Church (No. 2358) explicitly states that gay people "must be accepted with respect, compassion, and sensitivity" and that "every sign of unjust discrimination in their regard should be avoided."
The differences are manifesting themselves elsewhere, as well.
For example, the Southern Cross editorial blasted as "astonishing" a claim last month by a retired Spanish bishop, Fernando Sebastian Aguilar, who said that homosexuality is a "defect" comparable to his own high blood pressure. Pope Francis is set to make Aguilar a cardinal later this month.
And, in Poland, the hierarchy has launched a full-scale assault on what it calls the "ideology of gender," a vague term it says is aimed at promoting homosexuality, among other things. The bishops' campaign has prompted a strong backlash from many in the Polish church.
In India, on the other hand, Cardinal Oswald Gracias of Mumbai, the leader of Indian Catholicism and one of Pope Francis' top advisers, last month came out strongly against a decision by the nation's high court to reinstate a ban on gay sex, which includes penalties of 10 years to life in prison.
"The Catholic Church does not want homosexuals to be treated as criminals," Gracias said, and cited the pope's words when asked about his approach to gay people. "The church stand is, 'Who am I to judge them?' as the Holy Father has said."
And this week in Ireland, Archbishop Diarmuid Martin of Dublin reacted to concerns over anti-gay comments in the media by saying that "anybody who doesn't show love towards gay and lesbian people is insulting God. They are not just homophobic if they do that they are actually Godophobic because God loves every one of those people."
Martin also lamented that church teaching can sometimes be used "in a homophobic way."
What's behind these high-level disagreements?
Church observers say part of it is a backlash against the new visibility of gay people in society and the corresponding push to grant them legal protections and rights they never had before.
But opposition to the legalization of some rights, such as gay marriage, has at times turned into support for criminalization, which Catholic teaching does not condone. In fact, during a 2009 debate over an earlier version of a Ugandan anti-gay bill, the Vatican announced that Pope Benedict XVI was "opposed to 'unjust discrimination' against gay men and lesbians," a statement apparently aimed at the Ugandan bill.
Similarly, the new criminalization measures have brought calls for Pope Francis to go beyond his supportive comments about gays and lesbians and directly condemn anti-gay laws. The most popular effort is a Twitter campaign that goes by the hashtag #PopeSpeakOut. Church observers wonder whether the pope's inclination to allow disputes to be settled locally may incline him to let the debate continue without his intervention.
The controversy over the anti-gay laws is most intense in Asia and especially Africa, where culture can trump theology when it comes to dealing with gay people, said the Rev. Thomas Reese, a Jesuit priest and columnist for National Catholic Reporter and author of "Inside the Vatican: The Politics and Organization of the Catholic Church."
But Reese said regional political realities can play a key role, too: Church leaders who support anti-gay laws often come from countries with large Muslim populations that also tend to support measures against homosexuality. The bishops may not want to do anything that would inflame tensions between the communities.
"I think they're afraid of the Muslim reaction, and I think they're afraid of the reaction of many of their own people," Reese said.
On the other hand, Reese added, at least the bishops are facing criticism from within their own ranks a benefit of the more free-wheeling style that Francis has brought to the papacy.
"This is progress," he said. "In the old days, bishops wouldn't criticize each other. Now we have the bishops talking to each other and some are saying, 'No, this isn't the direction the church ought to go.'"