Not to worry!
In 1964 in the US the Republican Presidential nomination was taken by Barry Goldwater, a conservative Senator. Goldwater was a fine man, and probably not as radical as he seemed, actually.
While a hair to the right of most Republicans, he was way, way to the right of all voters.
Moderate Republicans and all Democrats elected Lyndon Baines Johnson handily.
It wasn't as close as it seemed at the time of the nominations.
Arf