So why doesn't the GOP simply kick neo Nazi anti Semites out of their party???
Answer: Because doing so would offend every inbred hillbilly who would otherwise vote Red.
Well I've already explained that.
But perhaps one more time: Because Political Parties in the U.S.A. are not organized as they are in many other countries where it is a closed membership system the party needs to accept you and can throw you out. Further that candidates are chosen by the party. In the U.S. the sole requirement to be a party member is that you have turned up at your municipal registry of voters (and the office that actually performs this function differs across the U.S.) and stated that you want to enroll as a member of a political party according to the rules of that state (which mostly have to do with how rapidly you can switch party enrollment and how close to an election you can do so).
As to candidates since the early 20th century, the standard method has been the primary election. ANY member of a party can run in that party's primary election for a particular electoral office the winner becomes the party's candidate for that office in the General Election. Parties have no power to remove candidates.
Party Caucuses in legislative bodies do have the power to bar a particular member from their caucus, but that is as far as it goes. It is not a perfect system but it has worked for over two centuries.