This is a good discussion. Personally I would never do it, somehow it seems not quite right. However, I have a squirrel hunting friend who grew up in Kentucky and he tells me that decades ago shooting a nest was common practice.
But I think this is about a lot more than shooting squirrel nests. Lots of the things we do as hunters can be made to sound "shaky" or unethical. Personally I don't like the idea of dogs being set out to chase and then rip apart a fox or coyote. But I'll never criticize another hunting brother for hunting that way. Ever, period.
I hear lot's of conversations about shoot/don't shoot scenarios on deer, and of course those who choose not to shoot are much more moral than the guys who would shoot, right? Hmmmmm........
Yet those of us who bowhunt send arrows slicing through deer which run off to bleed to death, that's why we wait a while before tracking themm, right?
Good conversations make us think, and that's a good thing.