The issue is not only about prevalence but also how it is addressed. Society at large tends to be more prone to persecute pedophiles than religious communities.
That is not what I've found to be the case at all.
1. Taking pedophilia seriously is something very new in history. If you go back to, say, the 1950s in the US, what you found is people denying it happened, and minimizing it when they admitted it. That was across the board, religious, nominal, and non-religious people alike. If little Suzy told Mommy that Daddy was... Mommy would smack her and tell her to stop lying. Today, thank goodness, the culture is gradually changing, but there are still many living in the past. Even today, only 50-70% of police reports made result in prosecution.
2. All institutions, whether they are religious or secular, protect themselves from scandal. All of them. In every case of pedophilia being made known, whether it was Little League, or Boy Scouts, or USA Gymnastics, or a school, the leaders of the institution circled the wagons and covered it up. All of them.
Religious groups often view themselves as self-regulating entities and may not adhere to mandated reporting requirements, believing instead in
priest–penitent privilege. Most religious communities are male-dominated hierarchies, protecting males, hiding and perpetuating abuse. In contrast, the secular world has mandated reporting laws and makes efforts to address and prevent such issues.
All this is good. And we should add that religious institutions have gotten on board with this as well. I'll address the Catholic church since that scandal is the best known. The CC in the US now requires every person working for it, paid or volunteer, to complete a course in recognizing and reporting abuse. They run background checks on every worker, both paid and volunteer. Any priest or church worker credibly accused of abuse is permanently removed from ministry. Allegations of abuse must be reported to civil authorities. No place will ever be 100% safe, but I'd say that right now, the Catholic Church is probably one of the safest places for a kid to be.
By far, the most charity is provided through secular governments, not religious groups.
Excuse me? The government is paid for by the tax dollars of everyone, both secular AND religious. Our representatives are voted for by everyone, both secular AND religious. Government workers are both secular AND religious. I'm sorry, but you don't get to claim government aid as a ribbon for secular people.
If you really want compare, show me the atheist organizations that give heavily to charity. Does American Atheists give generously to feed the poor? Does the Freedom From Religion Foundation raise funds to house the homeless? Does the Secular Coalition for America visit the old and sick?