Indeed, Bill Clinton did disagree on some of the social aspects of neoliberalism, but that term has come to stand for just the economic side.
I agree that the analysis simplifies matters. But the question is whether the GOP leadership cares as much about the social wedge issues as about the free trade policies. Assuming the Republicans are cynical panderers, Democratic triangulation would take away the issues the Republicans care about most, the economic ones.
So while the GOP would still have its social conservative talking points, that party would be driven to madness because its substantive platform, the only one the Republicans had any intention of enacting (mainly through tax cuts for the rich and by taking a wrecking ball to effective government) would have been taken from them. Assuming US politics has become a business (having been captured on both sides of the aisle by economic neoliberalism), the Republican brand would have been badly damaged.