It absolutely was a cornerstone value for American liberals in the past.
A documentary about the director of the ACLU, back before the ACLU abandoned it's principles, looks at how far the organization went to protect the speech of literal Nazis. The ACLU winning a Supreme Court case for their right to hold a public protest march was widely celebrated by those on the left.
>[The First] Amendment assures that even the most odious among us (with “odious” being the term that we apply to those we loathe, but who might view us as odious) the right to express themselves either orally, in writing, or by demonstrating or marching.
It was the freedom to march that caused a major flare-up back in the late 1970s, when members of the American Nazi Party, in uniform and bedecked with their decorative swastikas and stormtrooper boots, applied for a permit to march through the town of Skokie, Illinois...
To Glasser and the ACLU leadership, including David Goldberger, who headed the local Illinois chapter, freedom of speech is meaningless if it is not accorded across-the-board to all those along the ideological spectrum.
https://www.wgbh.org/news/commentary/2020/10/22/mighty-ira-a...