Rod Dreher adroitely argues they should remain a core part of the movement.
Media people who answer this sort of question usually say the Republicans ought to ditch social conservatism — this, because they are social liberals who tend to be free marketers, and they have no particular problem with the bipartisan imperial foreign policy. There ought to be a socially conservative party. As a social conservative, I will concede that the coming demographic tsunami compels the GOP to start making changes on its staunch opposition to same-sex marriage. This dog ain’t gonna hunt for much longer. I wish it weren’t so, but nobody who has spent any time reading the polls or talking to anybody under the age of 30 should have illusions about this.
I would be willing to accept the party liberalizing somewhat on this issue, provided it adopted a staunch position of defending religious liberty in the coming pro-SSM legal environment. Many younger conservatives who support SSM may find it acceptable to firewall religious institutions from civil rights laws, if that is possible. Liberals, of course, would howl about this, but this could be the kind of compromise that younger conservatives could accept and defend. I can see wanting your gay friends to have the right to marry and enjoy the benefits of marriage, but also not wanting the Catholic school in town, say, to suffer legal sanction because of it.