White supremacists marching at the University of Virginia – does this reflect the university’s attitude?
The march, and even more so the violence, were strongly condemned by UVA. Here are some statements from the President of the university to that effect.

The mayor of Charlottesville condemned the march in even stronger terms, calling it “a cowardly parade of hatred, bigotry, racism, and intolerance.” Note that the protestors came from out of town; they chose Charlottesville because it was in the process of removing and renaming monuments to the city's white supremacist past.

The US has a very strong tradition of free speech; generally speaking, if some people want to march, it is difficult or impossible to stop them, even if you oppose the cause for which they stand.

In my opinion the violence reflects badly on the US as a whole, but not on Charlottesville or UVA in particular. Whether or not things get worse, no one can say. I certainly hope not.