"Due process" is a legal term, and doesn't necessarily affect the choice of resignation or the "court of the public opinion". Regarding whether or not those accused will be found guilty of a crime, of course due process and the presumption of innocence should apply. But that is mostly separate from the issue of whether the accused will admit to what they've done (and many have) and whether they will step down or be fired.
I tend to believe the accusations, yes, and more so when the accused does not deny them. When they do deny them, then it usually becomes one person's word vs. another. In that case I will await more evidence to make a decision.
I don't believe them all, no. I question the validity.
I'm reminded of the Salem Witchcraft Trials and the McCarthy Era accusations of communism -- careers and lives ruined as what seemed to be a frenzy ofaccusations occurred. I do believe many allegations are probably true but it also seems that anyone can say anything and they're automatically believed - - like in the Witchcraft and Communism trials. So much of this currently strikes me as a frenzy.