Yes. The left wants no speech, pronouns, terms, characterizations, thought etc. etc. etc. to be allowed that is not what they declare proper. And they have become increasingly militant in enforcing that rule in media, education, government, institutions, entertainment, on social media, even here at USMB.Yes, I thought I indicated that I was using "classical liberal" in a non-standard way. Perhaps a better phrase would be "traditional liberal".
But there is a connection between "classical liberalism" and "traditional/modern liberalism" and that is individualism. Individualism is probably an inevitable result of modernity, first of all economic modernity. And what we see with the modern Left is individualism taken to the extreme: the 'Me Generation'.
That's why it's so easy for young Leftists to close down conservative meetings on campus: they're offended by what the think the speaker might say, and anything that offends or upsets them has to be destroyed. The rights of others simply are not part of their mental calculus. (We're stuck with the words "Left" and "Right", unfortunately.)
The Old Communist Left -- those who saw the Soviet Union (or, later Mao's China) as their ideal society -- were also against free speech for their political opponents, but for a very different reason: they saw it as a necessary aspect of the class war they were fighting, and you don't allow the enemy to have newspapers in your territory while you're fighting a war.
Classical Liberals strongly defend anybody, even their enemy, against libel and slander or bullying and encourage civility in all of society, but otherwise promote free speech including ability to express thought, feelings, beliefs, opinion freely and without retribution.