I don't think it is off, Felas. I have often wondered about this myself. I had a relative (now dead sadly), let's call her Jane, that I was very close to. Her son Pete was a very troubled individual - dyspraxia, various behavioural difficulties, physically abusive father leading to suicide attempt in childhood, sexually assaulted round about the age of 11 by someone on the fringe of their social circle (think the sort of "scoutmaster" level of involvement in his life), substance abuse and alcohol problems as he grew older. Pete went on to groom and sexually abuse a young teenage girl when he was in his twenties. Sue stuck by him through all his various behaviours, but not in the sense of believing him innocent, rather in the sense of "he's had such a shitty life, and I am the only person in his corner."
After her death, I had a long think about what role I should play in his life. There is a Quaker set-up called (IIRC) circle of friends, where groups of (I think usually childless people) set up social circles for convicted child sex offenders after their release from prison - the idea is that by tying offenders into a community who offer them normal social interaction but without the chance for further offending, they are less likely to go underground, seek out the only company they can online in the form of other sex offenders, and reoffend. It seems to work to some degree.
In the end I wasn't able to keep in touch (due to having a child myself and on police advice).
That's a bit long-winded but I think my response is two-fold. I think if my DS were to be accused of rape in adulthood, my priors would be very different to what they would be for a random person. I'd be starting probably from a prior belief of at least 90% that he was telling the truth when he said he'd done it; I'd be much more sceptical (based on known statistics and studies of offending patterns) about some random stranger's protestations of innocence. But I would be prepared to change that initial opinion in the light of evidence. (I've actually watched a close friend go through this with regard to their partner - partner initially stuck to their story of "I've been a shit for being unfaithful, but it was just a rough sex game gone wrong..." - my friend initially gave their partner the benefit of the doubt, but then as the court case proceeded and it became abundantly clear that the partner was lying, distanced themself). So yes, I can imagine not believing my child's claims of innocence.
I hope that (like Sue) I'd still try to support him - in getting through his punishment, in keeping him embedded in society so he was less likely to reoffend. (I don't quite know how I'd handle a situation where my child was tried, found not guilty, but I felt on the basis of the evidence I'd seen in court that he'd got away with it. Before anyone jumps on me, remember the standards for a criminal conviction are incredibly high - beyond reasonable doubt - so it is quite possible to think the evidence makes it more likely than not that person X did crime Y, but not that it's proven beyond reasonable doubt that they did.)