I don't really see a grain of truth in this.
If you mean "white racists/bigots" as the "working class", then absolutely.
But on "culture wars", Dems have been fully in line with what most Americans actually think.
- Decades ago, inter-racial marriage wasn't popular, and illegal in many states. Dems pushed against that, and today it's supported by a vast majority of Americans
- Abortion rights are favored by 2/3 of all Americans, something the Dems are fully in line with and that today's GOP is trying to take away
- Gays were mostly hidden away in the dark corners of America prior to the 1980s. Today, most Americans fully believe in gay rights.
- Gay marriage was also outlawed across most of America; today most Americans believe in gay marriage rights, because they've recognized that it has nothing to do with them, personally and doesn't harm them in any way.
- EDIT: add in gun regulations and limits on assault weapons, which most Americans favor, but the GOP cannot allow in order to maintain their NRA gravy train. And, again, conservative media reframes the issue as though "all gun rights will disappear", which isn't remotely the case. Americans favor most of the common-sense laws Dems would like to put in place.
What has been amazing over the past decades is GOP framing of many of these things as though they are or should be controversial, and ginning up their base who does not favor any of them (the exact opposite of most mainstream Americans). And Murdoch, et al do a fantastic job of marketing to them and making those bigoted and unpopular positions seem "normal and mainstream".