We can win white racists and white Christian voters
I think we can win more white voters. In fact, I think we can even win white voters who hold beliefs that many here would consider to be grossly illiberal.
Voters often hold a mixture of different policy views. People will often rank these views within their own minds. I don't mean that they sit down and make a list of ten policy views with number one being their most important view and number ten being their least important view. But I do think that when it comes time to vote some views win out over others.
So let us use a hypothetical. You have two voters who are similar. Let us say two working-class, middle-aged white guys from the Rust Belt, both union members. Both of them hold discriminatory views about non-whites and Muslims.
Voter A ends up voting for the Republicans because his discriminatory beliefs take precedence over all of his other beliefs. He might realize that the Republicans are union busters and that his Social Security and Medicare might be in danger if the Republicans win but in his mind stopping the Muslims from forcing sharia law on us or deporting more Mexicans back to Mexico is more important so he votes for the GOP because they are “speaking his language” on those issues.
Voter B might hold the same views toward Muslims and Mexican immigrants that Voter A holds but Voter B is more worried about the health of his union and whether Social Security and Medicare will be available to him when he retires so he votes for the Democrats, even though he thinks the Democrats are too PC.
The same thing holds for other issues. Some white Christians are single-issue voters on abortion and overturning Roe v. Wade so they vote for the Republicans like clockwork. Other white Christians might oppose the Democratic stance on abortion but they may vote for the Democrats because they are not single-issue voters and have a more nuanced position on pro-life issues. For example, they might see opposition to the death penalty and support for universal healthcare as part of a broader pro-life position.
My last example pretty much describes me. I am a Catholic and I consider myself to be a pro-lifer but I vote for the Democrats because I think that when you look at the big picture, liberal values and policies are more consistently pro-life than the Republican platform that is only concerned with overturning Roe and not with healthcare for mothers and children, for example.
Now I am not saying that the party needs to stop fighting for social justice. Racism is a huge problem in this country and we need to fight racist messaging from the Right if we want to win more elections. We also need to do more to break the stranglehold that the Right has over religious discourse in this country. But in the meantime we can still win over voters who are not perfectly liberal on every issue. I know we can do this because to a large extent we already win over people with mixed beliefs. Even now our own base includes many people who are not entirely liberal on every issue. African-Americans, for example, tend to be more religious and socially conservative than other demographic groups but they are a key part of our base.
See this article on what Pew Research Center calls the “Faith and Family Left”: http://www.people-press.org/2014/06/26/typology-comparison/types/faith-and-family-left/
Of course, some people are truly hopeless. Some white Americans vote based on racial tribalism first and foremost. But I suspect that their numbers are not as large as many Democrats think.
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One of the worst was seeing little African American children picking a white doll when asked to pick the "good one". 
What a ridiculous question to ask little kids, though. I hope the social experimenters explained that to the kids later, but that wasn't shown if it happened.
