I find that generally it helps, counterintuitively, to start with what the DBT[1] literature calls "validation" - reassuring the person that their fear makes perfect sense in light of their priors.

You can call this "affirming the emotional truth of what they're saying" if you want, and -- here's a part that took me years to learn -- you can do it without being dishonest.

For example, dialog between Them (T) / You (Y):

T: I don't think I'll let my kids trick or treat this year, what with all these sickos putting razor blades in chocolate bars, and weed in gummy bears, and did you hear about those AIDS-infected needles being left in coin return slots? There's all this danger around, it's just so awful, what a horrible place this world is, I mean what kind of person poisons children? [etc for 5 more minutes]

Y: Yeah definitely, I see what you mean - there are so many really crazy and evil people in the world. I mean with these shootings, and bombings, it's like we never get a minute to just rest and not be scared of something!

T: Right, exactly!

Y: I'm trying to remember though, what was the halloween candy thing? I mean I thought I heard something in the 80s about that but it went away, or was a hoax or something. Did something happen last year?

T: Well I can't remember but I mean the news was just saying a minute ago to look out for marijuana-laced gummy bears

Y: Yeah, weed candy would be pretty bad. I tried edibles once and got pretty fucked up, I mean, it wasn't really a pleasant experience. But then, some people really seem to like it. .... wait a minute, drugs are expensive. who wastes them on random kids? ... Did the newssay they found some somewhere, or just that it was a thing that could theoretically happen?

T:

Y: And the other "scary candy" stuff - do you know ifthere are any stats on how often this happens? I mean I 'm sure somebody did it at some point, because people are insane, right, but considering the way idiots drive, I wouldn't be surprised if kids have a higher chance of getting picked off by a bad driver, than killer candy. Which is scary too of course, but I mean, we're already living with that, and don't keep them inside.

Actually come to think of it ... I can't think of a single case I've ever heard of where an actual specific kid got hurt from poisoned candy. Maybe there are a bunch of em but it's kind of weird that we wouldn't have at least some detail - was it a boy or a girl, where in the country, how old etc? I mean it would have to be all over the news if it happened, so I wonder if this is just one of those cases where the media likes to scare the shit out of everyone all the time to get attention?

T: I don't know, it still seems dangers

Y: Yeah, I mean, we should all take reasonable precautions in the world and stuff, but ... tell you what, let's google for reports of poisoned candy from last year and if it's really low, then figure we probably have better odds than from bad drivers, and let the kids have their fun?

T: ok

[off to google you go, snopes is first-ish hit followed by other less entry-level but more-authoritative sources, and pretty soon they're coming around]

===

It certainly doesn't work that way every time, or even most times, but it can. And this has applications far beyond halloween candy. (Dungeons and Dragons. Immigration. Drug legalization. Rock music. Video games.) The person probably isn't insane; they probably heard a bunch of scary stuff, and got scared. Telling them "don't be scared" isn't going to help, but joining them on their side of the fence, then guiding toward a different outcome (which may not change their initial thought much but may help them change their behavior, which gives them more data on safety/etc with which to update their mental model for future use) can be pretty effective.

[1] https://en.wikipedia.org/wiki/Dialectical_behavior_therapy -- Though DBT was developed to treat BPD (see link for more), the recommendations for learning/teaching emotional coping skills seem to generalize well to many other kinds of emotional reactions that seem disproportionate to a given stimulus.