On page 34 of their 2008 report Licensed to Hug: How Child Protection Policies Are Poisoning the Relationship Between the Generations and Damaging the Voluntary Sector, authors Frank Furedi & Jennie Bristow make the following bold claim (emphasis mine, quotes-within-the-quote from David Pearson of the Churches' Child Protection Advisory Service (CCPAS), now known as Thirtyone:eight):
While most organisations working with children are able to vet each adult who will come into contact with children, the church, by its very nature, 'holds its doors open to anyone'. It is known that church congregations do attract sex offenders, 'so inevitably people are coming in all the time who are in contact with children'.
However, the claim is as bold as the supporting evidence is un-cited.
Scandals involving sex offenders within church hierarchies are well-known, but I've never heard of the claim that they are prevelant within congregations too. I'm not even sure how you would determine this, as most churchgoers probably wouldn't be open about their sex offending (unless, I suppose, they were required to be by law).
The only relevant article I could find is this one which discusses the prevelance of sex offenders within various institutions, including churches, and includes the following quote from 'University of South Australia emeritus professor Freda Briggs':
Paedophiles are attracted to positions where there are children, and celibacy is no impediment to them because they're not likely to fall in love with women and get married. And, of course, also, paedophiles like to be in a position where they have power and authority, and being a priest enables you to do that...The Church is, psychologically, a good place for paedophiles because church congregations tend to think the best of people, are not suspicious, and even convicted child-sex offenders have been allowed back into the Church and even allowed back into where they are in programs for children and in choirs.
However this again seems to be talking about those in positions of power rather than lay congregants. Also, the article is from 2013.