I'm go one further and suggest that many young people think government already can limit free speech. From campus speech codes to protests where reporters are forced out, I don't think this is at all surprising.
Jesse Singal from NY Mag offers some suggestions as to what this new data might mean:
But what exactly does 40 percent mean here? Is it a lot? It's hard to say for two reasons. One is that, as a Pew spokesperson noted in an email, this is the first time the polling firm has asked this question. This makes longitudinal comparisons impossible. It could be the case that there's something unique about millennials that makes them more open to supporting restrictions on free speech; it could also be the case that young people are always more open to this idea, but naturally age out of it, or that there's significant bouncing up and down from generation to generation.
It would also be interesting to see what these results would have looked like if the pollsters had chopped off the last two words, and made the question simply about speech that was "offensive" rather than "offensive to minorities." Survey results are notoriously sensitive to slight changes in question wording, and people don't necessarily hold coherent ideas about "offensive" speech. Plenty of folks freak out about anti-cop sentiments but are fine with racially loaded language, for example — or insert your own examples.