The racists who are prominent today, calling themselves the alt-right, also call themselves nationalists. They think this legitimizes themselves. "I am just a nationalist, defending my nation." There is something to this, but it is, of course, mostly ignorant bullshit. Huh?
The politics of any country is in part a competition about defining who the "us" is and what it means to be "us". And each nationalism has many threads or ideas, and groups will compete to highlight certain threads and ideas at the expense of others. The white supremacists want to emphasize race as the defining character of American nationalism--whites are American and no one else really is.
While whites have dominated the US, its nationalism has long been considered to be civil and not ethnic. Not focused on race but on the ideas contained within the Constitution, the Declaration of Independence and all that. Which has led parties to compete to define certain elements of those documents as being more or less important relative to others. Is freedom about the pursuit of happiness or is it about equal protection? While minorities may complain that this civic nationalism glossed over white supremacy, many minorities leaders embrace the elements of civic nationalism that promise better outcomes for their groups. What made Martin Luther King so very powerful was his invoking of the civic nationalism and calling white Americans to live by it.
The white supremacists who call themselves nationalists have a crappy understanding of history which undermines their claims. How can you be an American nationalist and be nostalgic about the Confederacy. The Confederacy aimed to destroy the Union and was very much treason. So, how can American nationalists venerate traitors? By focusing on ethnic ties--being white. But this nostalgia creates incoherence, which is fine for these folks because logic, facts, coherence are all irrelevant to them. Indeed, being ignorant is a point of pride with these folks.
Anyhow, getting back to the white supremacists, they call themselves nationalists, thinking this sounds good. However, the postcold war world has generally considered the nationalists to be problems--that these are the folks who spawn conflict. When they call themselves American nationalists, it only resonates among themselves and not any further. It sounds strange to the rest of America. Alt right? It might sound a bit better than Nazi or White Supremacist, but that is not saying much. The more people hear what Breitbart has on its site, the more disgusted they will be. Because intolerance of everything is actually un-American. The white supremacists will lose the contest to define American nationalism because the United States is actually a pretty successful place with a bunch of flaws, but a place where Latinos, African-Americans, Asian-Americans, immigrants, LGBT, Jews, and others can thrive. And their thriving really pisses off the alt right.
By calling Trump out as a racist and highlighting the alt right racists, Hillary may be giving them the press they want. But the exposure to the light will lead to political outcomes that they don't want--more years of Democrats, more years of empowered minorities, more problems for a Republican party that has to choose whether to get votes from Real America or lose national elections again and again.