|Note: Y-axis runs from 20% to 50% in the graphic|
We're increasingly a nation united when it comes to stamping out HateSpeech! in the public square. This petition on Change.org is something putative moderates at The Hill and True Conservatives at National Review are presumably on board with.
Given the runaway inflation in what constitutes racism (specifically that blacks are "inferior" in the context of this GSS question) since the seventies--to the point that tens of millions of Americans now believe voting for the winning presidential candidate is evidence of it--we might expect support for a blanket restriction on it to have lessened over time.
To the contrary, it appears we're a decade or two away from an outright majority opposing the first amendment. If you're relying on centuries-old parchment to hold the line against civilizational collapse, you're clinging to straws while drowning.
On the other hand, this data only runs through 2014. There's plenty of reason to think that 2016 is the year everything changed. When the GSS releases results from the Current Year just ended it will be interesting to see if we're able to detect a reversal in the trend towards restricting free speech.
GSS variables used: SPKRAC, YEAR(1970-1979,1980-1989,1990-1999,2000-2009,2010-2014), AGE(18-39), POLVIEWS(1-3,4,5-7)