Why would the Republicans back this initiative? The governor can't control redistricting and it will be really difficult for the democrats to retake the state senate and the state house!
Politicians are acutely aware of how volatile their profession is; I'm sure the NC Republicans remembers very well that the 2010 election turned a 30D-20R Senate split and 68D-52R House split into divisions of 31R-19D and 68R-52D, respectively, and that this unexpected sweep allowed the GOP to make their own gerrymander for the current decade. They know from experience that they can't predict how well a gerrymander can hold for an entire decade, and all but the most newly elected Republicans remember what it was like to be stuck in a minority party.
In the North Carolina situation, passing a bill for nonpartisan redistricting is essentially an agreement to a ceasefire. Both parties have gratuitously abused reapportionment powers when they've had the opportunity, and so now have both faced the other side of it, and now from that experience agree to play "fair."
Of course, "nonpartisan" redistricting is never truly impartial, but it creates a bright line limiting where and how reapportionment battles are to be fought, and even in cases of bias would prevent maps from being excessively hackish.