I think what a lot of people are fighting for is to not have these claims dismissed or undermined with quips like, "why did you take so long to come forward? she just wants money!" and other questions intended to undermine the accuser.
That's not to say we automatically assume the guilt of the accused. The accused should always get a legitimate trial, where innocent until proven guilty is the standard. But we should take the accusers accusations seriously until all the evidence is presented. I think that's a fair request; these people want to be heard and not dismissed.
I find it interesting that when someone claims they were abused as a child, especially by a religious figure, we entirely take them at their word until proven otherwise. That's what folks are fighting for, IMO.
But I agree that we have to be very careful about tarnishing reputations, and certainly some people take it too far and behave in a way towards the accused that's unfair and unjust.
People who make false accusations are doing massive amounts of irreparable damage to the accused and to actual victims.