The GOP doesn't need to drop its relative social conservatism, it needs to slowly shift wedge issues away from immigration, gay marriage and abortion and towards a new set of cultural differences that could win over second generation newcomers. I'd suggest drug use and liberal arts education as scapegoats.
This. Plus I think the shift needs to include religious liberty, which means making some outreach to immigrants who may not be evangelical, or even Christian. The role of religion in both the home and workplace is demonized by the left, which is not a comfortable idea to many immigrants, and the GOP does little to capitalize on this. Most immigrants to Canada vote conservative (barring a few majority-minority ridings where all parties pander to immigrants) & I fail to see why the same couldn't be accomplished in the US.
Also interesting (at least to me) is that the Conservative Party of Canada maintains a pro-life and anti-gay marriage platform. However, they promised to not legislate on these issues. The GOP could do the same, and leave the nitty gritty to each state to decide which is the right legislation for their constituents.
The key immigrant groups that the Republican Party needs to win over don't believe in the "our religious beliefs are under attack" meme though.
