This has often stumped me. Not being a world-traveler, I don't know how widespread this pronunciation is, but if anyone knows: where did the r come from?
I looked at spelling in print over the last century. This NGram chart gives the an exaggerated impression of the difference. Usage figures are 160,000 for sherbet, and 28,500 for sherbert.
That's more than 1 in 6 actually writing the r, almost certainly in contravention of what they'd find if they'd looked it up in whatever dictionary they had to hand. One could reasonably assume at least that fraction would say it that way, if not many more.
OP implies the less common form is simply 'wrong', but I see no reason to think this. It's just an alternative spelling associated with alternative pronunciation. So far as I can see, that alternative spelling has been around for several hundred years, so I guess the pronunciation has too.
Another very similar example is the pronunciation perservere for the standard persevere.
This is a famous example of
with a smattering of
The phenomena (not yet an explanation of why) is the addition of a sound (the epenthesis ), and the sound added is by assimilation (specifically progressive assimilation meaning the first sound affects the second).
As to why, well, it doesn't always happen, and in fact the opposite often happens (dissimilation, e.g. apeture for aperture, govenor for governor (note that this is for pronunciation not spelling)). So predicting when it will happen is not so clear. But we know, by the existence of other examples, that the phenomenon is not isolated.