(CNN) When leaders of the country's two largest religious groups -- the Catholic Church and Southern Baptist Convention -- hold meetings this week, the separate conferences will have a common agenda: clergy sexual abuse.

The U.S. Conference of Catholic Bishops, which represents some 51 million American Catholics , will hold their four-day spring meeting in Baltimore starting Tuesday. Meanwhile the Southern Baptist Convention, which counts some 15 million members , kicks off their annual meeting Tuesday in Birmingham, Alabama.

After a series of internal investigations and journalistic exposes, both denominations are reeling from scandals that have stained their reputations and demoralized the faithful.

"The cumulative effect of all the scandals does weigh very heavy on your soul," said John Gehring, Catholic program director at the Washington-based group Faith in Public Life.

"For many of us, it is getting increasingly hard to keep faith in the institution itself."

Gehring is far from alone in questioning the Catholic Church. A Gallup poll released in March found that more than 1 in 3 American Catholics say they have thought about leaving the fold because of the clergy sex abuse scandal.

Neither are Catholics alone in seeing their spiritual leaders commit or cover up heinous crimes, said Russell Moore, president of the Southern Baptists' Ethics and Religious Liberty Commission.

Messengers worship at the 2018 annual meeting of the Southern Baptist Convention in Dallas.

"Several years ago when I would raise this issue there was a sense of invulnerability," said Moore. "A church member might say that clergy abuse is a Catholic problem, or that it never happens in his church. I very rarely hear that now."

That's after Houston Chronicle and the San Antonio Express-News published a series of shocking reports about abuse in Southern Baptist circles. About 380 Southern Baptist leaders and volunteers have faced allegations of sexual misconduct, according to the two Texas newspapers, which also found that in the past 20 years, more than 700 victims have been abused, with some urged to have abortions and forgive their abusers.

On Friday, leaders of the Southern Baptist Convention released a 52-page report about abuse in the denomination, including survivors' stories and mea culpas about mistakes church leaders have made.

"We lament the fact that it took a national movement of reckoning for abuse to force us to take this issue seriously in our own convention," reads the report, conducted by advisors to SBC President Pastor J.D. Greear.

"It should now be obvious that the problem has been and still is more widespread than anyone has realized," the report continues, "affecting our congregations all over the country, from the smallest church pastored by a bi-vocational minister to the megachurch with hundreds on staff."

For both the Catholic bishops and Southern Baptists, the debate will likely center on the tension between autonomy and accountability. Traditionally, bishops and Baptists pastors have been allowed to operate in isolation, free from oversight. In the wake of these sex scandals, many of the faithful are now demanding change.

Bishops in Baltimore: Seeking more accountability

The goal for the Catholic bishops in Baltimore, is, simply stated, is to stanch the bleeding. The church spent much of 2018 suffering through a morass of scandals and this year hasn't been much easier.

In recent weeks, an internal report revealed that the US Catholic Church had spent more than $300 million on abuse-related costs from June 2017-June 2018, even before the latest iterations of the scandal escalated last summer.

The Catholic Church is trying to move beyond its abuse scandals of recent years.

On June 5, the AP published an expose accusing Houston's Cardinal Daniel DiNardo, president of the U.S. Conference of Catholic Bishops, of mishandling an abuse case involving an adult. DiNardo has vigorously denied the charges.

DiNardo, who suffered a stroke in March, has also faced accusations that he mishandled another clergy abuse case. Last November, police raided the cardinal's Houston headquarters , looking for "secret archives" related to a priest who has been accused of sexually abusing children. DiNardo has denied wrongdoing in that case as well.

"It is very hard to see how the conference can continue this way, with a president who is even worse than a lame duck," said Massimo Faggioli, a church historian at Villanova University in Pennsylvania. "The credibility of the US bishops is in freefall, which can only be stopped by a visible change in leadership."

A spokesman for DiNardo denied an interview request.

The bishops' reputations took another hit last week when an internal church report obtained by the Washington Post accused West Virginia's former bishop of sexually harassing young priests and spending hundreds of thousands of dollars on luxury items and gifts to powerful clerics. Bishop Michael Bransfield, who was removed from ministry last March, denied the accusations, saying he looks forward to his Vatican trial.

Even the Bransfield report was stained by scandal.

Baltimore's Archbishop William Lori, who led the investigation into Bransfield under a new church model to oversee bishops, apologized for editing the report to omit the fact that he and other bishops had received tens of thousands of dollars as gifts from Bransfield. He pledged to return $7,500 to West Virginia Catholic charities.

"If I had to do it over again, especially at a time when we are trying to create greater accountability and transparency, the report would've included the names of those bishops who received gifts, including my own," Lori said in a video statement.

At their semi-annual meeting in Baltimore, accountability for bishops is expected to dominate the agenda.

Traditionally, bishops have held a great deal of autonomy in their diocese, with only the Pope providing oversight. But the bishops are expected to debate several proposals to add new layers of accountability. The bishops had originally planned to take up these proposals last November, before the Vatican asked them to wait for further guidance.

Catholic bishops pray in St. Peter's Square at the Vatican.

That guidance finally arrived in May, when Pope Francis issued new, churchwide rules for reporting abuse in the Catholic Church. Among other things, those rules require bishops around the world to adopt new measures to hold one another accountable.

In Baltimore, the bishops are expected to debate several proposals to do just that: a third-party system to report abuse or misconduct by bishops; a way for bishops to investigate those reports; a new policy to discipline bishops who have already retired or been removed from ministry; and finally, a promise to hold themselves accountable.

But some already say the proposals will not satisfy Catholics eager to see their bishops held accountable, especially since the bishops themselves will be running the investigations.

"I don't see how that's going to satisfy the laity," said Francesco Cesareo, chair of the U.S. Conference of Catholic Bishops National Review Board.

Baptists in Birmingham: Fighting 'casual indifference'

Like the Catholic bishops, Southern Baptists say they don't just have to combat abuse -- they also have to change the culture that allowed such abuse to quietly continue.

"The cause of sexual abuse in the SBC is rooted in our culture of casual indifference to predatory sexual behavior," wrote Susan Codone, an abuse survivor from Georgia, in the report issued last Friday. "This indifference is the expressionless face of denial and silence."

Like Catholic bishops, Southern Baptists pastors work without much oversight from other church leaders. Each congregation is considered autonomous, with the pastor free to do what he wills. That autonomy has been used to avoid taking "appropriate action" against abusive clergy, the Southern Baptist report said.

At their meeting in Birmingham, thousands of Southern Baptist delegates -- known as Messengers -- will vote on proposals to introduce new measures of accountability. One would change the Southern Baptist Convention's constitution to list "indifference to sexual abuse" claims and racism as reasons a church can be booted from the SBC.

J.D. Greear, president of the Southern Baptist Convention, speaks during a preliminary meeting at the group's annual gathering Monday in Birmingham, Alabama.

Indifference, according to the proposal, would include employing a convicted sex offender, allowing a convicted sex offender to work as a volunteer with children, employing someone who covered up sex crimes and willfully disregarding child abuse reporting laws.

Another proposal would create a year-round committee to field misconduct claims. Right now, those complaints are only handled during annual meetings, when the Southern Baptist Convention is officially in session, said Moore.

Rachael Denhollander, an abuse survivor and advocate, has worked for a year on Southern Baptist President Greear's committee to address sexual abuse. She called the proposals to be debated in Birmingham "foundational steps."

"But the foundations will only be as good as what is built upon it," Denhollander said.

Denhollander, who is not a Southern Baptist, called for the SBC to conduct a study of abuse in its churches.

"It's very hard to solve a problem that you haven't yet diagnosed," she said.