I am unaware that Stalin was particularly xenophobe, but if he was that as well, then yes, the term may apply. Either way, the so called communist states are hardly a realisation of Marx' model, but are merely using terms from left ideology to establish an authoritarian regime which goes contrary to the idea of the ruling of the proletariat.
He was pretty xenophobic, heck, appeals to anti-semitism is available as well. However, I doubt you'll find any professors agree to use the label nazi for him.
What does Marx's vision has to do with anything, we're using your expanded definitions, we don't need to understand the historical context of Marx' model then, the word has after all been synonymous with the Soviet Union.
I agree that the terms I used do not differentiate the economical aspects of left and right, but I maintain that the term used as I do his helpful because it is isolating the problematic common core of traditional nazism and current day right extremism, which exists both, in neoliberal and fiscally social variants.
The common core for you seems to be quite a general one, imo. Xenophobia is such a weird term to use, because it often can fail at being an apt description and it can often function as a way to shut down criticism. Are one speaking of a rational or an irrational fear? If we refute cultural and moral relativism, it should be said in itself that fear of something strange or foreign shouldn't be a term of absolute certainty, but in which one has to understand the specific context of its use.
The biological aspect was bullshit anyway and the differentiation was at its core an ethnical one, with a huge emphasis on religion and nationality.
The biological aspect was technically bullshit, but it's not reality and rationality that's driving white nationalists, neo-nazis and white supremacists. Ethnicity isn't really a good term either, if you view the biological aspect of it as not important. I'd say the term was very specifically connected to the biological aspect and a sense of german cultural superiority. That doesn't mean that one can discount a sense of cultural superiority as being connected to nazism, unless we all want to go the route of cultural relativism.
Nationalism is the believe of the superiority of citizens of one nation (possibly limited by what you accept as a citizen, so people who migrated may be excluded) due to past achievements or societal structure and the ascribtion of achievements of people within the group to the whole group. Independent of being indigenous or not, the advantages are the following: and the disadvantages are seperatism, discrimination, exclusive behaviour, misplaced pride, and in many cases direct or indirect violence.
Your definition of nationalism could be ascribed to one part of nationalism yes, it's also the identification of a specific people as well. Minorities have clinged to the concept of their nation, especially indigenous people. There's numerous sources of Sami people recognizing themselves as a nation, a nation worthy of existence and living as their own particular people. Of course, the Norwegian State, even ran by rather left-wing people, was solely focused on assimilating them into Norwegian culture and recognizing them all as Norwegians, teaching them Norwegian. On the Swedish side you had the concept of Sami being ignorantly connected to excoticism and a prejudice to being Sami being equal to being a nomadic reindeer herder, while language was discounted.
I would point out that your definition, in order for it to be bad, would have to support itself on a sense of cultural and moral relativism. If seeing one's own nation as being superior to another one would be considered bad. Would it be nationalism to believe that Norway was superior to Nazi-Germany, to take a ridiculous example?
In your definition you're not connecting violence to nationalism, even if you are saying it is connected to it. Are you saying it's a consequence of it? If so, what about other isms, like capitalism, might that also cause cases of violence either directly or indirectly? I can imagine in some cases it would, due to the distribution of resources.
The demand to stop migration, throw out asylum seekers and to take away legal rights that protect asylum seekers, basically revoking rights that are guaranteed by the constitution.
So, understanding this, if someone wants to stop migration and views the asylum institution as bad, they're akin to a nazi? Constitutions can be amended, as people on the left in the US tells me. That's without considering whether all of those account for the people you're talking about, which I'm not seeing much proof and I hope if there is proof, it's not based on anecdotes.
My point in all of this is your dubious use and convenient use of the word "nazi". If people were to listen to you explain your definition of the word and hear it repeated often, it loses the gravitas that the origin of the word has. Sure you can expand and change words, but that also changes the effect of the word itself. You could change nazi to mean "people who love their country" if you wanted, but that doesn't mean that the semantic change carries over its previous gravitas and inherits its historical meaning.
My disagreement on you in regards to nazi, regards to the same disagreement I have previously had with the right wing americans using the word "socialist" or "communist". Sure, they can expand the term if they want, but they just look like simpletons and they don't understand the importance of a term in regards to its historical context. If you go around calling more and more people nazis, it certainly won't do a lot of good for those who've had family members or their country affected by nazi doctrine. It's laziness, that's what it is, because in the end there are probably more apt words you want to use, but you want to hitchhike on the gravitas of the term instead. It's just a populism, but from the left.