Most Americans and Europeans will support "Terrorist" censorship. The U.S. giants are under pressure from Germany's Chancellor Merkel and soon probably President Trump to effectively censor the net. They've come together to create a database of hashtags that can reliably detect repostings in today's systems. They can be worked around with a little work, but many posters are too lazy to do so or don't have the expertise. Details in the Facebook post below.
Hillary Clinton is an example of the many "liberals" who have joined "conservatives" calling for limits on speech for those labeled "terrorists." Unfortunately, no one can agree on who is a "terrorist." The Turkish government labels some Kurdish groups "terrorists" while the United States sends arms to their close allies in Syria and Iraq. The term has become almost meaningless. The U.S. free speech standard - that almost everything is protected except an immediate call to violence - seems better to me. ("Clear and present danger.")
I doubt more than 10% of people in Europe and the United States are near-absolutist in a free speech debate. One reason I do is I have a clear perception of the slippery slope.