I think most people are troubled when they think the government is engaged in political activism or campaigning -- in fact it's illegal. So it's a difficult questions to answer, and you didn't directly answer it: "to what extent governments should be in the business of
building solidarity and shared values?" You just identified the results of shared values or lack there of.
If the majority of voters do not want the government to build solidarity, or to build it against the status quo, then the only way the government can legitimately pursue such an agenda is to label it a constitutional or human right. And that is indeed the language we see used by some to promote universal health care or a living wage.
My pet theory is that homogeneity of culture makes it easier to share wealth.