Fortunately the two events will occur in the order they that they will. Having a reference will help explain the issue.
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.