Alt right is the semi Jewish friendly anti-immigrant, anti-Muslim kosher racism that was too big for tea party Republicans.
New right was the attempted revival of racism through libertarianism and National Socialist literature.
Both are right as they both oppose democracy and equality (title of Tom Sunic’s book).
New right is not just opposed to Jews, but also the ideologies they use. There is no good answer for whether they are pro Israel or pro-Christian, because racism is the primary issue.