Improving the situation of celibate pedophiles requires changing hearts and minds of non-pedophiles ("nons"). These nons cover a spectrum.
Some just would hate an attraction to children without much thought, because it's bad. Some who thought a little might hate it because it violates the moral principle of "purity".
Others hear of the existence of celibate pedophiles and are instantly on board. The way they think society should work is that no one is condemned based on their group membersip. Every individual needs to be treated as an individual, and every one given the benefit of the doubt. So they may have never considered that there could be celibate pedophiles, but as soon as they hear of their existence, then they are accepting. If we do not harm others, then to them we are just as good as anyone else. What we fantasize about is nobody's business.
What about the middle? The existence of a few celibate pedophiles doesn't settle the question. They want to hear of a large group of people who they can connect with at some important levels -- people who are like them in the ways that matter most. I will try to paint a picture of this group. One important advantage of this exercise is that I do not need to own and explain the behavior of all pedophiles -- just some of them. I have often tried to characterize pedophiles by saying we cover the same range on just about any attribute you can think of as other people. Yes, a very few pedophiles murder children -- a very few ordinary men murder adults. A few are serial molesters -- a few ordinary men are serial rapists. Some molest a child who seems willing. Some men have problems with consent, an issue that has received more attention in recent years. (Many pedophiles are not exclusively attracted to children, and have some level of attraction to adults. But I will set them aside here and continue with the simpler case -- they have no sexual attraction to adults at all.)
So where do we start? A pedophile realizes they are sexually attracted to children by roughly age 16 or so. Their first reaction is horror and self-hatred. They have this reaction because they hate child sex abuse just as much as you do. This should be no surprise -- they were raised in the same society, and they are not a psychopath. A big factor in intensifying this horror is the myth in society that all pedophiles will offend. They fear they have a progressive mental illness, and while they may be fiercely protective of children now, they fear that over time the mental illness will erode their moral compass and their self-control. Many figure they should kill themselves to protect the children. We have no good statistics on how many teen suicides are in fact pedophiles, but a great many muddle through. Some retain this self-hatred throughout their lives. They hate this sexual desire for children, even if they never act on it. Many "nons" who have little sympathy for pedophiles can see why it's a good idea if these people are offered therapy if they fear they might molest a child. That much sympathy and acceptance is good, but I hope for more.
But the other group, the sympathetic group I am trying to portray, realizes that their attraction to children is something they did not choose and cannot change, and just like any other undesirable unchosen trait, that cannot be their fault. They continue to hate child sex abuse, and initially are deeply distressed at the idea that they might molest a child. They get an increasing measure of peace as they become increasingly certain they never will. Nons may wonder how they can be certain they will never molest a child. Sexual desire is powerful, and how plausible is it that any but the tiniest group of people can give up for life the prospect of sex with another person?
Consider the group of ordinary adult-attracted men who can't get a date. It's reasonable to assume that many never visit a prostitute (cost, legal risk, not truly satisfying). Suppose we also rewind history to before 1950, when pornography was not readily available. They might look at calendar girls and masturbate, but the vast majority of them never, ever raped a woman. Modern "Incel" is a disturbing trend where men resent this fact and try to claim sex as a right, but the positive spin on this situation is that this is in reaction to the ongoing reality where many such men never get to have sex. Unspoken is that so few in this class satisfy their desire for sex by raping women that they don't change the basic picture of "men who can't get a date".
One old observation in psychology is the "approach-avoidance" conflict. They both want to get something but are also afraid to get it. At a distance, desire is stronger and makes them approach, but the avoidance aspect rises more steeply as they get too close. They may be stuck at a certain distance. For most humans, however strong a desire is for sex, it is ultimately less powerful than a desire not to hurt another person. This is precisely the situation facing most pedophiles. Some, of course, do not understand (or choose to ignore) the harm they could cause, but they are not part of my sympathetic group. A large group of pedophiles understands children enough to know that sex is likely to cause them lasting harm, and however strong their desire, they are like the rest of people unwilling to harm anyone for sexual satisfaction.
Another challenge some ordinary people face is a specific person in their lives who they are strongly attracted to but who is off limits. A woman might be the boss's wife, or your best friend's wife, or any woman who is happily married in the typical exclusive marriage. While affairs do occur, a great deal of the time the attracted person simply lives with the attraction and never acts on it. This is especially likely if the object of attraction is not interested. A great many pedophiles will similarly succeed in avoiding sexual activity when there are specific children in their lives they are attracted to.
So a pedophile in the group I am portraying has no attraction to adults, and knows they will never do anything sexual with a child, and they are nonetheless accepting of their sexual desire. Let's suppose that they are content with partial satisfaction of their desire through masturbation. The use of child pornography is a large issue here, but let's restrict ourselves to the large group who never looks at child porn. They are unwilling to get satisfaction from the record of a real child's sexual abuse. What are their fantasies like? Since child sex abuse is terrible, and they are fantasizing about child sex abuse, isn't that sadistic?
It usually is not in the least. The child is simply transformed in the fantasy into a willing participant who would not be harmed in any way. Adults do this regularly. A man fantasizing about a model or movie star knows (if they stop to consider) that the chances are basically zero that this woman would want to have sex with them. So if they fantasize about her, are they fantasizing about rape? Usually not. They have simply performed a small adjustment to the woman when incorporating her into their fantasy. The same goes for a hot woman in a man's life who he is pretty sure would not take kindly to his advances or perhaps has rebuffed actual advances. Do we say this man is fantasizing about rape if he fantasizes about this woman? No. His fantasy is harmless. It is not hard to transform a child in the imagination in the same way. Children are often affectionate and interested in friendly touch, and those genuine qualities are enough to make the required transformation in fantasy especially easy.
So let me summarize this pedophile who I hope many people will find sympathetic. He never comes close to molesting children, and let me elaborate just a bit. If you earnestly ask an ordinary man if he's sure he'll never rape a woman, he is likely to be somewhat offended. The pedophiles I have in mind would react the same way, for the same reason. Thi spedophile finds some children attractive. When he is alone, he may transform the memories of some children into willing or even eager participants for purposes of fantasy and the partial sexual satisfaction that is the limit of his sex life. No long-term harm accrues to the fantasy child. Also, zooming the camera back a long way... a great many people through most of their lives find meaning and purpose in activities that have nothing to do with sex. Pedophiles also have all those opportunities available to them to make a satisfying life.
I hope I have sketched for readers a large group of pedophiles who are pretty much like anyone else when it comes to moral compass, a conviction that sex is bad for children, and self control. They are attracted to some of those children, but -- like other people who can't get a date -- they make do without partner sex, and have no real temptation to seek sexual satisfaction by harming anyone else.