Republicans don't need to "soften their stance" on social issues.
They simply need to realize that not every issue needs to be subject to law.
Politics, ultimately, is the stuff of law-making. This is certainly how the voters view it.
So unless you are proposing laws, you shouldn't be talking.
If Republicans want to be the party of less government, then that needs to be more than just a slogan. Rather than seeing what new crevices government can stick its nose in, Republicans should be actively restraining government. Discarding unnecessary laws, and preventing congress from passing new ones.
Surprisingly, to the unsophisticated voter, the GOP is the party of restrictions, not Democrats!
Repubs must step back and figure out how that is.