Often, the demands of the protesters have seemed to conflict with the principles of freedom of speech and of the press, such as when students (and one faculty member) blocked media access to a public space at Missouri and when one group of protesters demanded that the media publicly endorse them at Smith College in Massachusetts.
To outside observers, these demands were often confusing. Given the overlap between the cause and the activists, though, perhaps it shouldn't be.
Pew asked various groups of people whether or not it was appropriate for the government to intervene to censor offensive comments about minority groups. In the United States, no two groups were more sympathetic to letting the government do so than millennials (defined here as those aged 18 to 34) and non-whites.
Millennials were actually about as likely to endorse some censorship at rates greater than countries that have no 1st Amendment or its equivalent. The biggest spread among Americans was between millennials and members of the Silent Generation — those aged 70 or over. There's overlap there with political affiliation, of course; Democrats and Republicans differed greatly. (Why Germany saw the greatest willingness to censor negative commentary about minorities should be obvious.)
If we paint with broad strokes, we can see how this overlaps with what's happening on college campuses. Young people and people of color support limiting free speech when the target is offensive comments about minorities.
The situation at these schools is more complex than a struggle between free speech and emotional safety. When it comes to assessing why that struggle is happening and why certain groups are on one side or the other, though, these data offer some insight.