roadbikeRob saidThe first order of business for the GOP is to evict all the narrow minded bible thumping screwballs and reactionary rejects.
You are right, but such a move would probably reduce their electorate by a third or more. A three party system; Democrats, Republicans and 'New Republicans' would probably work fine at the local, state and Congressional levels, but it might mean the Democrats retaining the presidency for decades. Given the president appoints SCOTUS justices, America would probably continue on a progressive path for generations.
Also factoring-in future demographics, I'd say the GOP is pretty much screwed for the foreseeable future, regardless of whether it splits or continues in its current form.