Why? If I think that the democratic decision is wrong then I'm going to want it undermined. If we voted for slavery then I'm going to want it undermined. If we voted for a decision that would lead to a recession then I'm going to want it undermined. — Michael
I agree with you.
The democratic process is open-ended, after all. "The People" never speak once and for all time. Take prohibition in the United States. Prohibition was passed with the support of a particular demographic -- rural, native, midwestern, anti-alcohol voters. The anti-prohibition demographic (rural, Northeastern, immigrant, and pro-alcohol) was not sufficiently mobilized. 13 years later, the ill effects of prohibition, and the dissatisfactions of the pro-alcohol demographic, were sufficient to result in overturning an earlier popular decision.
Were drinkers wrong in persisting in their use of alcohol during prohibition? Legally, yes. The People had spoken; prohibition was the law of the land.
The problem with prohibition is that the will of only one (minority) set of voters was adequately expressed. For many native-born Americans and immigrant communities alcohol was an important component of conviviality and socializing. Catholics and Lutherans both used wine in worship, for instance. Most Protestants didn't (and still don't).
The decision on EU participation is likely to be determined by which demographic gets to the polls. If a larger portion of older voters opts for Brexit, and the usual lesser number of younger voters is not at the polls to pass Stay, then you'll be out. Is that fair? Technically, yes: Majority rule. On the other hand, it isn't fair for older people (for whatever reason) to cut off what the younger generation sees as a necessary component of their future.
So yes: legislative decisions and popular referenda are open to challenge. Only if the new law is clearly immoral (like extending slavery to new territories, or requiring people in free states to facilitate slave recapture) is open defiance acceptable. Many people considered prohibition an intolerable imposition and disobeyed it. At various times and in various places, immoral laws have been openly flouted while efforts were made to change the law.
When should one accept law one doesn't like? When it isn't clearly immoral, or illegal. When it is passed with a large enough majority to be incapable of overturning. The courts decided that referenda results and laws passed denying gay people marriage were illegal, even if they were passed by huge majorities. So, over many an unwilling voter, gay marriage is now law, like it or not. Is this now carved in stone? Well, probably not. A different court and differently worded law could change things. Before 1973, abortion was a settled -- and usually illegal -- question. After Roe Vs. Wade ('73), abortion was resettled on the side of being legal everywhere, like it or not. 40 odd years later, the issue is becoming unsettled -- with moves toward illegality, again, like it or not.