In order to be considered "racially" jewish, they must have a jewish mother.

If you make a lot of money, have influence, and do a lot of signalling that you support Jews they will accept you as Jewish if you have a Jewish father. They will just more readily reject you if you don't have a Jewish mother. Jewish mother is like the fast pass. You can also convert to Judaism but it's a long drawn out process (drawn out on purpose so that it's limited to a small amount of people). So Judaism is absolutely a genetic group more than a religion.

What do you consider people who are the opposite of that with a Jewish father and white/european mother?

They are all potential Jews and therefore should be treated with extreme caution. Often more caution then full Jews because they can act as subversives and spys. That's why the Jewish community encourages some of their members to out breed and assimilate. They need people they can tap to lead Jewish efforts in certain exclusive businesses, religion, institutions, etc. The Jewish community admits to these things. It's not the alt right that's excluding these people as white. It's the Jewish community themselves that for generations consistently act in their own interest instead of the local interest or the nations interests. Don't try to frame this as the alt right being violent or radically exclusionary. We would have gladly assimilated Jews if they had actually WANTED to assimilate. Instead they used our good will against us. Small levels of assimilation are not that dangerous to large racial groups. Hitler's Nuremberg laws were actually quite lenient towards quarter and half Jews.

How would half jewish people be treated under an alt right regime?

I would propose a similar program to the 1935 Nuremberg laws in NSDAP Germany. Those laws would be equivalent to a slow cleanse (i.e. very few people would actually be physically removed right away). Hitler created a core Germanic group and a 'people's community' buffer zone group. It was actually quite brilliant. The people's community could marry inner group people but there were some rules around it.

Greg Johnson has his own version. You can read more about this here:

https://counter-currents.com/2014/06/the-slow-cleanse/

edit. Inb4 OP or someone else accuses the alt right of 'evil ethnic cleansing'. Ethnic cleansing is being done to us in a much more brutal way with a goal of world domination and enslavement of ALL races. The slow cleanse proposed here is to re-establish lands already stolen and to create a counter to Jewish international domination and slave engineering. I do not propose an expansion or cleansing of Asia or central Africa or the middle east or any other part of the world that is non white. I would also consider changing my slow cleanse position if all hard and soft ethnic cleansing against whites was ceased immediately and right of association was granted back to whites.