We are lucky that the Y2k issue was so understandable by the public. I doubt we will have such luck addressing the Y2038 problem.
I'm seriously thinking of hibernating through the 30 days covering Y2038.
But I would argue that there is also a much higher proportion of individuals who do not understand technology and who are out of the loop on this kind of thing.
Of the remainder, perhaps half don't really have an opinion.
The remaining 25% vaguely accept that it was a real problem, but are not at all aware of the real extent.
Anecdata, to be sure, but you might want to spread your net more widely when asking people what they think.
As someone who was forced to spend Y2K in a "prepped" cabin on the side of a mountain with two years of supplies buried underneath, I think you might overestimate the quality of the public's response to Y2K.
The public did not maturely understand that software needed to be updated and everything was OK.
There was some real panic out there. It was arguably the biggest "End Times" event of the modern era, definitely IMO surpassing "2012" and other "apocalypse panics".
The Y2k preppers and panic, I think, was the foundation for the modern prepper movement and the public's desire to flip from conspiracy to conspiracy to predict collapse.
I think you might be using an unusual description of "the public"
https://www.livescience.com/46123-many-americans-creationist...
People who believe that the earth evolved over time due to a completely natural process is mostly gaining ground through losses to "god guided evolution" not young earthers who are going strong.