I couldn't find the original page I was getting those numbers from, but here's another that gives a bit more granularity. It does seem like that 25% number interprets "sexual abuse" very broadly, but the more detailed numbers are still horrifying and still cause for alertness.
A last note: I agree that it is impossible to tell from a few hours of interaction whether someone will abuse your child. Many people can't tell even after years of loving marriage whether their spouse will abuse their children, so "demonstrating acceptable qualities" is not a very good intervention. The absolute best defense against one's children having unwanted/traumatic interactions is to tell them how to set boundaries, tell them to yell if they're touched in a way they don't want, tell them that their body is their own and that nobody gets to touch it without their permission. This has the virtue of defending against all manner of abuse and mistreatment, at the hands of parents, extended family, family friends and acquaintances alike.
Indeed, I didn't say "this is a horrible idea, Alicorn." I was just trying to mention this consideration, which I was a bit surprised not to see mentioned in the original post. If the children are all well-educated about how to respond to attempted abuse, and the adults all know this, a strongly abuse-deterring environment is created.
Rationalists like to live in group houses. We are also as a subculture moving more and more into a child-having phase of our lives. These things don't cooperate super well - I live in a four bedroom house because we like having roommates and guests, but if we have three kids and don't make them share we will in a few years have no spare rooms at all. This is frustrating in part because amenable roommates are incredibly useful as alloparents if you value things like "going to the bathroom unaccompanied" and "eating food without being screamed at", neither of which are reasonable "get a friend to drive for ten minutes to spell me" situations. Meanwhile there are also people we like living around who don't want to cohabit with a small child, which is completely reasonable, small children are not for everyone.
For this and other complaints ("househunting sucks", "I can't drive and need private space but want friends accessible", whatever) the ideal solution seems to be somewhere along the spectrum between "a street with a lot of rationalists living on it" (no rationalist-friendly entity controls all those houses and it's easy for minor fluctuations to wreck the intentional community thing) and "a dorm" (sorta hard to get access to those once you're out of college, usually not enough kitchens or space for adult life). There's a name for a thing halfway between those, at least in German - "baugruppe" - buuuuut this would require community or sympathetic-individual control of a space and the money to convert it if it's not already baugruppe-shaped.
Maybe if I complain about this in public a millionaire will step forward or we'll be able to come up with a coherent enough vision to crowdfund it or something. I think there is easily enough demand for a couple of ten-to-twenty-adult baugruppen (one in the east bay and one in the south bay) or even more/larger, if the structures materialized. Here are some bulleted lists.
Desiderata:
Obstacles:
Please share this wherever rationalists may be looking; it's definitely the sort of thing better done with more eyes on it.