Pope Francis, flying back to Italy after his trip to Brazil, was asked by reporters about a Vatican monsignor who had been accused of having a same-sex relationship while living in Latin America.

"If someone is gay and he searches for the Lord and has good will, who am I to judge?" Francis answered.

Suggesting that gay people should be forgiven for their actions won't exactly win Francis a GLAAD award. But it's certainly an olive branch to the gay community, especially considering the document signed by Francis' predecessor, Pope Benedict XVI, that said people with deep-rooted homosexual tendencies should not be allowed to be priests.

Pope Francis' Brazil trip did plenty more to give hope to religious liberals, too, as he stressed that the wealthy should do more to reduce income inequality and said that the Catholic Church was "perhaps too cold, too caught up with itself, perhaps a prisoner of its own rigid formulas."

(MORE: The rise of the religious left)

Before his week-long trip to Brazil for "World Youth Day," Francis had already raised the ire of Catholic traditionalists by washing the feet of a Serbian Muslim woman and saying that God redeems "even the atheists."

In May, he told a crowd at St. Peter's Square in Vatican City, "I think about those who are unemployed often because of an economic conception of society that seeks egoistic profit regardless of social justice" — a statement that union official Damon Silvers said was "very similar to our message at the AFL-CIO."

These incidents, as well as Francis' relative silence when it comes to condemning abortion, gay marriage, and birth control, haven't pleased traditionalists in the Catholic Church.

"This is already true of the right wing of the church," Archbishop Charles Chaput of Philadelphia told the National Catholic Reporter. "They generally have not been really happy about his election, from what I've been able to read and to understand."

The editorial board of The Independent wonders if the pope is really looking to shift the Church's "attitude to homosexuality, to women priests, to contraception, abortion, stem cell research — all those toxic issues that no pontiff until now has dared to confront." That's unlikely though, the paper notes, as the conservative College of Cardinals chose Francis to become pope in the first place, suggesting he's hardly a liberal.

Conservative blogger John Zuhlsdorf, a.k.a. Father Z, questions whether liberals really ought to be so happy about the pope's seemingly progressive bent, noting that "by projecting a compassionate image, he will simultaneously make it harder for them to criticize him when he reaffirms the doctrinal points they want him to overturn."

Ultimately, hoping for a complete turnaround on hot-button social issues might be too much for progressives to ask for. That doesn't mean, however, that liberals should dismiss Francis, Neera Tanden, president of the Center for American Progress, tells TPM.

"As a progressive I think the pope kinda rocks," says Tanden. "The fact that he's been so aggressive on social justice is something all progressives should welcome."