Socially conservative from the point of the country as a whole, maybe. But socially conservative in terms of the Republican Party, maybe not.
What I mean, is even when swing voters consider themselves socially conservative they won't always vote for the most socially conservative Republicans.
Those voters are socially conservative in comparison with liberal Democrats, but can be pretty moderate in comparison with the most conservative Republicans.
Also, they may respond well to pro-life and pro-family themes, but not to Republican economic policies.
We've seen this before with very devout minority voters who still vote heavily for Democrats. No reason to think that would change anytime soon.
That's true, but the Republicans are trying to appeal to the opposite, the socially liberal, well-off, white voters who might like conservative economic policy. Trouble is they're violating conservative orthodoxy by changing their views on social conservatism. It's a much more natural fit for the party to seek out minority voters, especially since we don't have to change our economic policy much if it all, but simply explain stuff like the "trickle-down" theory better. And, arguably, the Hispanic voters are the most important demographic we need to appeal to going forward.
To hang on to those socially liberal voters later, they need to abandon their social conservative principles pretty much completely and permanently. To get minority voters, as well as any remaining white Reagan Democrat types, we ought to be able to stick to all our principles, and simply work on the marketing and messaging of our economic views. Our economic philosophies result in a better country for all.