You are going further than the judge did. The Judge never said he believes the abuse happened.

Mr. Allen's relationship with Dylan remains unresolved. The evidence suggests that it is unlikely that he could be successfully prosecuted for sexual abuse. I am less certain, however, than is the Yale‐ New Haven team, that the evidence proves conclusively that there was no sexual abuse.   ... I agree with Dr. Herman and Dr. Brodzinsky that we will probably never know what occurred on August 4, 1992. The credible testimony of Ms. Farrow, Dr. Coates, Dr. Leventhal and Mr. Allen does, however, prove that Mr. Allen's behavior toward Dylan was grossly inappropriate and that measures must be taken to protect her. ... After considering Ms. Farrow's position as the sole care‐taker of the children, the satisfactory fashion in which she has fulfilled that function, the parties' pre‐litigation acceptance that she continue in that capacity, and Mr. Allen's serious parental inadequacies, it is clear that the best interests of the children will be served by their continued custody with Ms. Farrow

"The Yale-New Haven Hospital Child Sex Abuse Clinic’s finding that Dylan had not been sexually molested, cited repeatedly by Allen’s attorneys, was not accepted as reliable by Judge Wilk, or by the Connecticut state prosecutor who originally commissioned them. The state prosecutor, Frank Maco, engaged the Yale-New Haven team to determine whether Dylan would be able to perceive facts correctly and be able to repeat her story on the witness stand. The panel consisted of two social workers and a pediatrician, Dr. John Leventhal, who signed off on the report but who never saw Dylan or Mia Farrow. No psychologists or psychiatrists were on the panel. The social workers never testified; the hospital team only presented a sworn deposition by Dr. Leventhal, who did not examine Dylan.

All the notes from the report were destroyed. Her confidentiality was then violated, and Allen held a news conference on the steps of Yale University to announce the results of the case. The report concluded Dylan had trouble distinguishing fantasy from reality. (For example, she had told them there were “dead heads” in the attic and called sunset “the magic hour.” In fact, Mia kept wigs from her movies on styrofoam blocks in a trunk in the attic.) The doctor subsequently backed down from his contention.

The Connecticut state police, the state attorney, and Judge Wilk all had serious reservations about the report’s reliability."

Soon-Yi Previn (born circa October 8, 1970) is the adopted daughter of actress Mia Farrow and musician André Previn, as well as the wife of filmmaker Woody Allen.

https://en.wikipedia.org/wiki/Soon-Yi_Previn

I certainly would not allow this man to get near any of my children.

This is pretty understandable.

nude photos of one of the young girls

We are still talking about Soon Yi here. She was grown woman at the time of these photos, 19 or 20. She was not a young girl.

We actually do know when their affair began. She was home from college and previously had never spent much time with Allen alone. Mia asked her to take Soon Yi to a basketball game and that's when they started.

I went to college in NJ, right in the NYC media market and remember everyone was following this pretty closely. This broke just as we were returning. I had a few journalism students in my dorm. They would break down which reporters were "Team Mia" and which were "Team Allen."

I believe even Mia said the affair started after Soon Yi came back from college and Mia encouraged Woody to take her to a Knicks game.

I remember when the gossip columns got that picture of the two of them at Knicks game that was a big story. One of the gossip columnists in a memoir talked about getting a picture of Soon Yi at college because there weren't many current pictures of her and it was not publically known where she went to college. They looked through the photos they had and saw her bag or her sweatshirt at an R on it and they went to Rutgers and other local colleges and then found her at Rider.

This is kind of the basic facts of the case. Allen's relationship with Soon Yi was skeevy but not illegal.

You can look at any of the news reports from when this came out to find her age. Lots of the NY papers from back then are online.

I just did a search and here's an article on Woody and Mia from the year before the scandal broke. So this is not rationalization afterwards.

http://www.nytimes.com/1991/02/24/magazine/woody-and-mia-a-new-york-story.html?pagewanted=all

She and Previn had three sons (Matthew, Sascha and Fletcher); then they adopted three orphan girls -- two Vietnamese (Lark and Daisy) and one Korean (Soon Yi). After their divorce, she adopted a Korean infant (Moses Amadeus Farrow), who has cerebral palsy. In 1985, Allen and Farrow adopted a newborn girl from Texas (Dylan O'Sullivan Farrow). Two years later, they had their own son (Satchel O'Sullivan Farrow, named after Satchel Paige, the baseball pitcher and a hero of Allen's; the last name was chosen because the couple didn't want one Allen among two Farrows and six Previns).

..... Allen and Farrow very much lead their own lives, while continuing a relationship that is the longest either has had. By any standard, it is not a conventional union. They are not married, neither do they live together; their apartments face each other across Central Park.

If you search "woody soon yi 1992" here's the descriptions from the summaries you see on the front page of google

...discovered sexually graphic Polaroids of her 19-year-old adopted daughter...... ..... an affair between Mr. Allen and Soon-Yi Previn, Ms. Farrow's 21-year-old adoptive daughter...... the relationship between her adopted daughter and Mr. Allen came to light when she discovered nude pictures of Ms. Previn, who was then 21,....Mar 20, 1993 - Mr. Allen, 57 years old, said that when he embarked on a sexual relationship with Soon-Yi Farrow Previn, 22, who was adopted by Ms. Farrow and her former husband, Andre Previn,.......Mr. Allen's romance with Soon-Yi Previn, 21 years old, whom Ms. Farrow adopted when she was married to.......while he was becoming involved with her 21-year-old adopted daughter, Soon-Yi Farrow Previn. .....Mr. Allen begins an affair with Soon-Yi Farrow Previn, the 21-year-old adopted daughter of Ms.