In my opinion, the discussion on multiculturalism has become somewhat distorted nowadays. In the history of mankind, people of different kind who are moving over vast territories has been the normal. This does not mean that migrations have always been peaceful as in-groups and out-groups have always existed. However, I think it is only with the creation of nation states that differences of origin have been articulated as much as it is now.
Fascism is in its nature a political movement that thinks the in-group is superior to other groups. With the existence of nation states it is very easy for fascist movements to draw the line along ethnic lines. The morally and culturally superior people is the ethnic majority of that state – the foreigner becomes the scapegoat. I do not think this has to do with the mixing of ‘races’ in the first place, but it is more about the logic of fascism.
Poland is a prime example of this. Before the second World War, Poles, Germans, Jews, Ukrainians, Lithuanians, and other people lived together on the territory on Poland. But after the war the country became one of the most homogenous countries in Europe because of the Holocaust and the following mass expulsion of people after the end of the war. But as we see today, this is not an antidote to fascist policies. Because there are no non-European immigrants to put the blame on in Poland, the far-right government has found new culprits to the in-group. In this case, the LGBTQ-community was targeted as LGBT-free zones were introduced and LGBTQ was described as an ideology, not real people.
Another example is Italian Jews who initially voted for and were members of Mussolini’s fascist party since they were not targeting Jews, but blaming other out-groups at first. But eventually, the Jews would be targeted as well and banned from the party (more to be read here -->
https://www.quest-cdecjournal.it/italys-fascist-jews-insights-on-an-unusual-scenario/).
As we can see, the problem with fascism is not multiculturalism, different religions, different sexual orientation or whoever the scapegoat is. The problem is the fascist ideology itself. The most important thing is to protect the weak groups in society - the poor, the sick - who groups like CasaPound target to get support among the general public.