They allowed their party name to be implicated in an ideology that in theory they do not endorse. This gives observers the impression that they are moving towards, or at least supporting, these views.
Eta: in practical terms, you are right and a sophisticated observer would get what happened. But branding is a real thing, and enough of it will give credence to the belief that Republicans are closet nazis.
In the UK, people have been expelled from political parties for bringing them into disrepute. As long as there is due process, I can't see why that can't work in the US.