I think Nikki Haley pushed for the removal of the Stars and Bars from state property in the wake of the Emanuel AME Church killings rather than the removal of monuments. That's a different and far more defensible position.
I'm not sure rank and file voters need to be doing political calculus on the issue to determine their feelings on a particular issue. However, it should inform the political priorities of high information voters, especially if they are influential and involved in party politics. And we voters should strive to take part in a truly representative debate and exchange between conservative & liberal & ethnic/religious minority & white interests rather than dwell in echo chambers and become radicalized/polarized. And in this particular case, if that was happening, then I think it'd take a lot of the starch out of the movement to take the monuments down as I do not think that Northern liberals have anywhere close to majority support behind them. It costs them political capital, and liberals need to do a far better job of picking where they spend that capital IMO, because we've been getting the **** kicked out of us on election day for the past 10 years.
Democrat politicians certainly need to do a better job of figuring out the political calculus on these issues. Especially in VA, where there is a gubernatorial election in a few months and the race will be close and Northam is not a particularly inspiring candidate. But the politicians dwell in the same echo chambers we do, and Democrats are trying to win support from an increasingly polarized and activist base too.
As for political sea changes on marriage equality and health care, those are interesting examples of what liberals get right, politically speaking. Though I would caution that we're not quite there on health care yet. The public only got behind the ACA in response to disastrous Republican alternatives, and I'm not sure the support for true reform to a single payer system is there yet. Hoping it comes eventually. Marriage equality is a good example of the appeal that the liberal principle of inclusivity and fairness can have in the electorate. "Dogmatically sourced arguments should not prevent LGBT people from having a fundamental civil right." Where liberals get into trouble is when they get too far away from their principle of universal inclusion and begin excluding and marginalizing other groups who disagree with their orthodoxy. And that's also true in the case of marriage equality, where we activate the Right against us by doing things like targeting and shutting down businesses who object to providing services to LGBT marriages on religious grounds. Liberals have this self-destructive tendency to overreach, far beyond the strength of our popular support, especially on social issues, and it just kills us outside of our base.