Hold on, you're confusing different viewpoints. The people who contributed stories to the site, and would be the ones to report to the police, are the alleged victims. From their perspective, there is no "presumed innocent". If they are telling the truth about having experienced abuse first-hand, then they
know he is guilty of at least their own abuse story and very likely the others, in which case the repercussions you mention would be well-deserved. If they are lying, then obviously their behavior is reprehensible regardless of what exactly the target suffers.
You go on to say that the peanut gallery - from which perspective "presumed innocent" makes more sense, though its level of applicability to public opinion is far from universally agreed on - should not believe the claims, because it has the potential to both cause injustice in this case and set a bad precedent for the future. That may or may not be true, but it doesn't really respond to the original question of "what would you do", if you were victimized yourself. Well, I suppose it can be seen to respond to some extent: if public shaming creates a bad precedent, that's a drawback even if a victim knows the shame is accurate; and if people respond as you suggest by distrusting these sorts of claims, then making them may do more harm than good to one's case, i.e. give people more ammunition to defend the accused with. (And of course that effect has occurred, though it's harder to say whether the site has done more good or harm overall.)
But that just establishes that public shaming has downsides. The problem is that all the other options suck too, if you're a victim of rape or lesser sexual abuse. Obviously doing nothing sucks; the major remaining option is involving the police. For one thing, if you're successful and end up with a public prosecution and trial, this will end up invoking the court of public opinion anyway, which will not necessarily be satisfied by a not-guilty verdict in real court. I suppose you can at least not actively encourage it, but privacy also has inherent downsides. Even if you have enough emotional strength yourself to face the justice system, face your abuser head-on - and that's a big if, statistically speaking, considering the low reporting rates in general estimated for rape - there may be other victims who do not, who may come forward with their stories, providing more evidence, but only if the case is publicized. And of course, if you don't have adequate proof, then the abuser will not be convicted regardless of your emotional state: which is good policy in general but which you know to be an injustice in your own case.
So what would you do? I don't think there's any good answer. Even if public shaming is the least sucky approach in some cases, that doesn't mean it's not problematic and worthy of criticism. It just means that it may deserve sympathy anyway.