Valka's attempts to insert the real world into my hypothetical example notwithstanding, I'll ask my question again:
How would you feel about Mr. X if he was a long time member of this forum and was accused in this way? What would go through your mind? Would you give him the benefit of the doubt? Or would you ostracize him?
I suspect most people might say, "It depends on who is doing the accusing and who is being accused."
I don't see how you can ask this and NOT consider what would happen in the "real world" if someone were to make such an accusation against a fellow forum member.
Over a decade ago on the RPG gaming forum I belonged to, there was a moderator who, before his appointment to staff, was completely upfront with the site owners, the admins, the other staff, and indeed everyone that he had been in prison, had served his time, and was trying to turn his life around. The fact that he's gay didn't seem to bother most people
until he was appointed to staff... and then suddenly there was "Think of the underage posters here! Think of the parents who won't let their kids buy your gaming magazine or other product anymore! Get rid of this gay moderator who is a convicted criminal!" hysteria flying around.
Some of us who defended this guy - who had never been in trouble at all since his sentence was completed, and who had been a very productive forum citizen (running PBP games, participating in the Iron Pen contests I ran there, being supportive to people who were feeling down in the dumps, encouraged new members, etc.) - were in turn accused of some really crazy and paranoid things... sometimes by the site owners themselves.
One of them dredged up as much of my personal RL information as he could find, posted it, and openly encouraged others to "contact" me. As in RL kind of contact of the sort that is not friendly. To make matters worse, someone found the blog of someone from my city who had the same name as me and posted her photograph - thinking it was me. In truth, the person whose photo was posted was a 17-year-old high school girl, and I was horrified at the possibility of any of these <unprintables> harassing her. I told the senior admin to get all of that off the forum NOW or I would be contacting the RCMP, informing them that an American gaming company was advocating harassment and who knows what else - basically putting a target on a kid who had my name, was not a member of that forum, and would probably get into a panic if she started receiving the vicious garbage that was being thrown at some of us for defending a moderator who had committed no crime since joining the forum but was being treated as though he had, or that he would somehow jump out at people off the computer screen.
The information was taken down, but the harassment did continue, up until the point a few years ago when I had to tell the game producer's wife on FB to leave me the hell alone.
Needless to say, I will not name that site, the company, or the people involved, since I don't want to give it ANY publicity. I no longer belong to that forum (I do belong to a couple of the ones that broke away in response, as some of us wanted nothing more to do with supporting site owners who would do that to its members), and haven't bought even a penny's worth of their gaming product since.
To answer your question... My choice would be "neither; let the admins sort it out". I'm completely serious in saying that I would expect the admins to handle it - ask each side for their story and deal with whatever consequences come with doxxing and decide what to do regarding a member accused without evidence.
The admins we have here are not like the ones at that other forum, who perpetrated or aided in perpetrating accusations against certain members and the other members figured, "If _____ and _____ say it, it must be true" and only a few of them bothered to ask any of us for our side(s) of the story.
I am also serious in asking if CFC actually has a policy about this kind of thing. Given the context of your hypothetical, it's a reasonable thing to ask about.
So if you object to me bringing RL into this, too bad. I don't see any way to
not consider RL issues in such a hypothetical.