It is certainly true that the majority of people who refer to themselves as republican are not extremists. It used to be the VAST majority, but that has changed as more republicans have left the party to avoid being lumped in with the crazies. Some call themselves Libertarians, though most of them don't really get what "real" libertarians positions are. Some call themselves independents. Some eschew any party affiliation at all, even when in fact they retain one. Those who they gave the power to, however, continue to do the nearly irreparable damage that their seats at the adult table allow them to do. Like Inhofe, McConnell and Cruz, and Graham and King they feel no fealty to the rules of conduct or the expectation of civility and compromise that our system of government is based on, and indeed needs to operate properly and for the benefit of it's citizens.
Those that remain "officially" in the party, while they may not themselves be extremists, seem perfectly willing to let the extremists represent and speak for them. They either don't get it or they don't care. Many are so uninvolved that they don't even realize what has happened to their party, and they just continue to do what they have always done, and vote for people who have an R after their name. This last, as stated elsewhere, is not wholly a republican problem.
It has always stunned me how competent republican pols have been in getting their followers to vote against their own interests. Chris Hayes once said "The republican party is a con and their base are the marks", and I believe that to be true. While only a very small portion of Rs, for example, are the very rich, R pols manage to get their rank and file to help them protect all their vast wealth from taxes. They get them to protect the large corporations whose benefits go almost exclusively to the rich from having to pay fair wages, protect the environment, or hide their money overseas so that taxes can be avoided. And even though the majority of rank and file Rs want women to get fair pay and to be left alone when visiting their doctor, want EVERYONE to be allowed to vote unencumbered (understanding that vote fraud is a fantasy), believe in evolution and science (including climate change), want sane gun laws and good competent public schools, they continue to vote for pols who stand for the opposite. Republicans LOVE to take advantage of what they know is an ill-informed electorate, and they do whatever they can to keep it that way. They are their own self-fulfilling prophesy.
I don't know how this get's fixed as it is a very difficult problem. The only solution I can see would be a huge risk for the American people, and I find it hard to imagine they will take it. And that would be to choose Hillary as President, and give both the Senate and the House back to the Democrats. Even if the American people chose that, it would be VERY difficult to make it happen given the gerrymandering that occurred after the 2010 election. The Rs have made it all but impossible for Ds to get the House back even when Ds have more votes, as they did in the last election. It can only happen if the rank and file Rs want to let it happen. Is that even possible? Is there anything we can do?