To explain why the alt right/neo-Nazi/Klan/whatever notion of "protecting white identity" is so toxic, one analogy comes to mind. Back when I was in high school, there was a bully who enjoyed antagonizing smaller students near the lockers. Usually he wouldn't get physical, but on the occasions when he would, his victims faced an awful conundrum: refuse to fight back and thus get humiliated, as well as possibly seriously injured, or fight back and thereby face punishment from teachers who invariably insisted that "both sides" were to blame?
In the paradigm of modern American politics, the individuals who talk about protecting "white heritage" are the bullies. When the people who aren't designated as white — African Americans, Hispanics, Jews, Muslims, and so on — mobilize to defend themselves, they do so in response to the bullying.
This doesn't mean that the latter groups are justified in resorting to violence. It does mean, however, that there is a significant and ineradicable difference between their cause and that of the white supremacists, one that prohibits informed individuals of good will from conflating the two.
Indeed, the very term "white" exists for the sole purpose of creating an artificial class of so-called "superior" people in America's social hierarchy. As I've explained in the past, historical scholars recognize that the construct of whiteness was invented to distinguish between the in-groups and out-groups in American social life. After the Civil War, it was reinforced by nationalists who wanted to unify America's diverse regions behind a common cause (namely, the preservation of "white" culture).
This isn't to say that there aren't individual nationalities which are considered "white" today that don't have their own heritage of which to be proud.
You can be rightly proud of being German or Irish or Polish or Italian or Greek. After all, those are nations which have their own rich histories and, when it comes to the United States, have developed their own subcultures with equally fascinating histories of their own.
Yet the fact that each of the groups I just listed was, at one time or another, also deemed "non-white" in this country proves the larger point about how the concept of whiteness is fundamentally toxic because it exists only to exclude. While an American of German descent may be considered white today, this was not the case during World War I; while an American of Irish descent may be considered white today, this wasn't the case when New York Gov. Al Smith and Massachusetts Sen. John Kennedy ran for president in 1928 and 1960.
In short, when white supremacists like the now-infamous Peter Cvjetanovic insist that they only marched in Charlottesville to argue that "white European culture has a right to be here just like every other culture," they are using code language to cover up their true agenda. Similarly, when President Donald Trump argues that the people protesting against white supremacism are morally equivalent to those protesting in favor of it, he is at best ignorant of the history behind "whiteness" and at worst disingenuously trying to conceal his actual sinister belief system.
Every man, woman and child has a right to be proud of their heritage, but no one has a right to oppress others based on that pride. Yet anyone who advocates in favor of white identity is doing precisely that, and as such must be met with the condemnation of decent human beings everywhere.