Occasionally when dealing with irrational people I have found it useful to match their energy level. So if they're yelling, you start raising your voice too. And you take whatever it is they're saying seriously . And if you have an objection, you state that objection. Then you continue the argument until the raised voices seem pointless and you both just calm down. I had to learn this technique when I was living with…
His example was a tailor of very high-end clothes, think tuxedos that cost as much as most folks' cars, custom women's jackets for formal events, etc. A customer comes in, angry that a button is sewed on with an incorrect thread pattern. Something to fix if you're paying $10,000 for a jacket but not exactly something reasonable to get angry about. The customer comes in, throws the jacket on the counter and demands that it be fixed. Rather than trying to de-escalate their anger, be absolutely outraged that one of your employees would do this. Assure the customer that you will find out who did something so inconceivably stupid, and that you will most certainly fire them on the spot. The expected response will generally be something like "well, it's not that big of a deal I mean if we just fix the threading..."
I'm sure there have been exceptions for other folks but every time I've used this tactic (generally reserved for the most egregiously ridiculous displays of anger) it's worked almost immediately.