> The left side of the political spectrum has for a very long time advocated for an interpretation of 1A that is "free as in liberty" while the right prefers a "free as in anarchy" approach.

You may have it backwards, depending on one's definitions of "left" and "right". It was Berkley's Free Speech Movement, largely composed of leftist students and sympathizers, that kickstarted the "free as in anarchy" approach to speech in its modern incarnation. And anarchy is not even an exaggeration as many of its members occupied buildings, engaged in shut-ins and shut downs of privately owned businesses, as well as mounted police cars when one of their members were arrested. In many ways, this is the style of freedom the internet offered at its earliest and most fringe.