Moving to the center on social issues won't help the GOP. It'll just send their white working class voters into the hands of the Democrats, who actually would do a better job representing them anyway, at least on pocketbook issues. If the Republicans want to make themselves electable and make inroads with minorities, they don't need to move to the left on social issues. Rather, they need to stop being the elected patrons of plutocratic privilege.
Of course that will never happen. The Republicans have been in plutocracy's grip since 1876, and every time they nominate a reformer (T.R., Ike) they ultimately get outmaneuvered by the bone-headed business elites that want to drag the country back into the Gilded Age. If by some miracle the GOP could move to the center on economics, or even the center-left, they'd have a good shot at rebuilding themselves as a mass party, conservative social positions or not.
I've heard the opposite argument made also: that when the Democrats moved towards the center on economic issues in the '90s, it sent their lunchpail voters into the hands of the Republicans.
Former Congressman Dan Glickman (D-Kansas) did an interview for something a few years ago and he mentioned that a rural white guy came up to him in 1994 and told him why he wasn't voting for him. He basically said that Glickman supported NAFTA which he saw as a threat to the livelihood of him and people like him. Furthermore, he and people like him were/are very socially conservative. So, if forced to choose between a party that was wrong on social issues and economic issues (the Democrats), and one that was just wrong on economic issues (the Republicans), he was going to go with the Republicans.
Low-income whites generally fall into one of two categories: the "angry" ones who want to lash out at someone to make them feel better about their situation, and the "hopeless" ones who figure they're screwed, their parents had a miserable, hardscrabble life and their children and grandchildren will have miserable, hardscrabble lives, and usually don't even bother voting.
Even if the angry ones don't like the GOP's move to the center socially, where are they going to go? The Democrats don't want them and shouldn't want them. They can win elections without them and, quite frankly, the rest of their coalition - the educated, the minorities - aren't going to want to be in the same party with those people.
