You have to laugh at people defending the salute as Roman. It is a widely recognized fact that the NAZIs modelled themselves on the Roman empire, right down to the rallies, the Swastika flags held aloft ala the Roman standard, the eagle etc etc.
Rome is not a nice empire to model yourself upon, the enslavement of hundreds of thousands of non Romans, the crucifiction of Christians, the rape and subjugation of the 'Roman world'.
Ergo the Nazi Empire stole their salute, there is no nicety about saying that salute is Roman.
I am sorry but people are idiots.