As a society in general, repentance often is assumed on profession of a desire to change, rather than an actual demonstration of change, but that is a terrible standard. Any seasoned liar can cry on command and be convincing; any good con man can explain his actions just as convincingly. Some things are serious enough that we have to take them seriously, no matter how we feel about the person in every other aspect of his life. Sometimes, skepticism has to be the foundation, even though that goes against the ideal for which we strive in all other areas of our lives.
Also, some things are serious enough that repentance needs to include an acceptance of a complete prohibition on the situations that caused the sin in the first place. Those who have abused children should be excluded from any situation where they are alone with children. Period. Professed (or even genuine) repentance notwithstanding. To the end of their mortal lives. No possibility of parole. Period. We can believe their assertions of a changed heart, but we need not create situations where what they did can happen again. Someone who truly has repented sincerely and completely, and who is truly humble, will understand that societal need for certainty and gladly acquiesce. In fact, that is one of the truest fruits of repentance, imo - the humility to change “normal activity” to submit to the best interests of society. If someone fights such a restriction, arguing against it in any way, even by claiming full repentance, I believe we must retain a degree of skepticism and be even more diligent in our duty to protect the innocent.
Some things are serious enough that they need to be categorized outside the norm and treated differently. Jesus himself categorized the abuse of children as so heinous that painful death is better than what will happen to the abusers. That came from the one who said, "Neither do I condemn thee" to a woman caught violating one of the most serious commandments of the time. If he was willing to avoid condemning the adulteress but spoke so severely about child abuse, I think it requires a different approach than other issues.
"Forgiveness" is one thing; ignorance and acceptance of ongoing temptation is quite another; giving the impression of more concern for the perpetrator than the victim(s) is still another. Some things simply are so horrific that they deserve a life sentence, repentance notwithstanding - and anyone who truly is repentant will understand and accept that need. Again, if they fight that restriction, they aren't sufficiently humble to recognize the need for it - which means their heart really hasn't been changed fully - which means there still exists at least a sliver of possibility that it will happen again, given extreme pressures and the perfect storm.
Think of an alcoholic or a drug addict. It is a central, fundamental tenet of rehabilitation that such a person must accept the need for eternal diligence - abstaining from any situation where alcohol or drugs are flowing freely, particularly where there is no support structure to help avoid temptation. That is the manifestation of real repentance - the willingness to do absolutely anything in one's power to avoid any situation where past mistakes are a legitimate possibility. If a drunk or drug addict won't commit to avoiding bars and crack houses, why must we accept their promise that they are the exception - that there simply is no way they will succumb even if they go dancing with the devil?
Again, someone who has repented fully will understand that; someone who has not, will not.
I could pray and ask God this question: "Should I call this man who has sexually abused his daughters to be the Primary Teacher in his daughter's class?" If I did, I would expect one of two answers: 1) total silence for asking such a stupid question; or 2) a solid, spiritual slap upside my head for asking such a stupid question.
Finally, we conflate forgiveness with love WAY too much. They are NOT the same thing, and misunderstanding forgiveness plays a HUGE part of the problem in this type of discussion. Suffice it to say that, unless an abuser has abused me, my wife, my children or someone close to me, forgiveness is not my right. It is left to those whom he has harmed in a real way. "Easy forgiveness" does not help the abuser - and it can be devastating to the victim and those close to the victim, who of necessity will struggle greatly to be able to do what appears to be so easy for us. "Easy forgiveness" of this sort is a result of ignorance and misunderstanding, and it needs to be rooted out of our lives in every iteration. Pure forgiveness is wonderful; easy and indiscriminate forgiveness is abominable.