Here's the scenario.  You're running an event, and on TWITter or Fecesbook, someone calls out a guest and states, "I wouldn't feel safe with this person at the con!"
You must immediately ban this person from the convention.
No, not the guest. The person making the public scene.
Here's why:
This person is arrogating a lot of significance to themselves. The statement assumes that the guest in question either knows this person or will seek them out, and has time allotted for the purpose of interacting with them, any desire to do so, and such interaction must be negative. All of which are almost certainly utterly false assumptions.
For myself, it doesn't matter to me one way or the other how the complainant feels. Their statement alone makes it clear that interacting with such a person is of utterly no interest or consequence to me. I can find much better people to interact with. Actually, let me rephrase that: I can find PEOPLE to interact with.
In fact, they're almost certainly well aware they're perfectly safe, and attempting to drive political opposition into the shadows.
Well, no one ever accused Nazis of honesty.
Furthermore, they've passively-aggressively created an interaction where none existed.
They have, in fact, created an interaction with the guest, and an interaction with you, in a public scene.  Imagine if they walked up to you (or the guest) at the con, and shouted, "STOP HARASSING ME!"
You must assume their intent is to lay groundwork to CREATE a scene they can attempt to blame the guest, or you, for.
In reality, no professional should feel safe with such a person at a convention, and since the professional is the draw, not the nobody, the nobody should be immediately banned for the safety of the guest, the staff, and the other attendees.
Because, if you actually have a legitimate issue with someone, here's how it is handled, speaking from experience.
Most conventions ask their guests in surveys, privately, "Is there anyone you don't want to be on a panel with?"
I have a very short list of people who I simply can't get along with. If the convention wants to put them on a panel, I can do a different one. No harm, no foul.
There was one time when I did have a legitimate legal issue with another person (long resolved, it was merely administrative).  What I did was contact the event PRIVATELY, inform them of the issue, and tell them, "This person is not to approach my booth, and I will not approach theirs.  I do not anticipate trouble, but if they enter my booth I will shout for security at once as a safety measure for us both."
In one case, I actually was harassed by an individual whose stated purpose in showing up at the con was to harass certain "conservatives," me among them, even though I am not conservative. I went quietly to Con Ops, explained the issue, and the individual was informed not to approach me or my family again.
In no case did I whine like a worthless fucking attention whore to the world, pointing a finger like a body snatcher and shrieking like an angry toddler.
As we've seen at least three times now, knuckling under to this type of crybully is like trying to appease a toddler or terrorist.  Once you give in once, you have delegated veto power to them and the TWITter dogpile.
At which point, the reasonable (non-public) response may become public itself, thus giving you...instant controversy.
Your only rational, immediate response to avoid "controversy" is just to ban the person making the public scene. They've already told you by this action that they intend to cause trouble for at least one of your guests and that guest's followers.
"I wouldn't feel safe with this person at the con!"
"We're sorry you feel that way.  Here's a full refund.* We hope to see you at a future event."
Then stop responding. You'll only give attention to an attention whore.
Having seen this happen to guests at least three times, any future guest invitations I accept will involve a signed cancellation clause and a cash penalty for doing so, because once a guest has made arrangements for your event, they can't schedule something else, and you're eating up their writing/art/production time. They are there for YOUR benefit, not you for theirs. In my case, I currently have three novels, a collection, an anthology, all contracted, another novel offer, three on spec, an article request, three short stories and a lengthy stack of products to test and review, and an entire summer of professional bookings. I have a not-quite four year old and a teenager. Don't waste my time then roll over for some worthless whiner.
 I encourage all other pros to implement the same policy. My attorney has a sample you can use.
*Assuming they've even reserved space or intended to, rather than just harassing your convention for "justice," as happened at least twice.
The guests are professionals. It's time the conventions started acting the same way.
ADDENDUM: I was contacted this morning (May 16, 2018 ) by a convention who is proactively taking this step. Of course, they're the type of convention for whom this would never be an issue. Which is why they're confident taking it.