Contrary to your story there was no panic, just a well planned and executed approach with enough safeguards to make sure we could deal with anything unexpected. I'm sure there were many other companies and organisations in the same situation.
At the time I was in banking - international trade finance, specifically. Being part of a multi-national banking group, and being in Australia, we were the focus of the years of preparation that went into making sure it wouldn't be a problem for the bank. Being a bank, there was also involvement in the programs and updates and changes and tests and so on that went with the entire financial industry here. I wasn't an IT person then, but lots of our (and my) staff were involved in testing and checking and so on. Some were even working right up to the stroke of midnight and a little beyond to make sure everything was fine and be available if it wasn't (to help the IT folks check and test and what not).
The time and money involved was massive.
If nothing had been done, it would have been a huge problem.
Funnily enough (perhaps not quite the right term, but run with it), there were scare mongers. Some of them even tried to get us to finance them with a "fix" they had invented. It was all a scam designed to play into the FUD and make them rich. They made up all sorts of scientific sounding terms and nonsense and peddled it to various financiers. Most of them just turned them down because they just didn't understand what was being peddled at them enough to give them the confidence to get into it but they didn't actually understand what it was, but when it came across my desk I realised what it was because, even then, I was a computer geek (I just happened to be a banker by profession). Anyway, a mate of mine had a mate who was in the fraud squad. They didn't enjoy their new millennium so much.
The point is that all sorts of people will believe all sorts of things, but what you really need to do is rely on someone who actually knows what they're talking about instead of those who say what you want to hear. I was the guy who knew what he was talking about in that case. In terms of climate change, I'm listening to the folks who know what they're talking about, and who happen to be in the vast majority. If they change their views because of new evidence, I'll keep listening and change, too, but it's foolhardy to not listen to them just because you don't like what they're saying or you think you know more than they do when you don't.