I did phones in a different century, so I don't know whether this would fly today. But, my go-to for someone like this was "ok, I think I see the problem here. Shall we go ahead and fix it or do you need to do more yelling first?"

I can't remember that line ever not shutting them down instantly. I never took it personally, whatever they had going on they were never angry at me personally.

Then again, I do remember firing a couple of customers ("we don't want your business any more etc") after I later became a manager and people were abusive to staff. So you could be right, also.