Tucker Carlson is lying and supporting the first amendment isn't "left wing".
During this same episode Tucker says that the First Amendment was inspired by Christianity and therefore since Charlie Kirk was a good Christian, he was the biggest supporter of the first amendment. Then Tucker plays a clip of Charlie Kirk telling a college student that she should be forced to carry a 2 week embryo to term, as evidence that Charlie was in support of the first amendment.
Does this line of reasoning make any sense to you? First Amendment = Christianity = Anti-abortion? If you're not a right winger, it probably doesn't. This is because words mean entirely different things to right wingers. To understand what they are saying, you have to interpret their words through their own framework.
Tucker Carlson engages in the same level of word salad as Kamala Harris or Mayor Pete. As a propagandist, the things that Tucker Carlson says are not meant to make sense, it is meant to engage the emotions of the audience, typically a right winger.
In the clip of the tweet, Tucker is only saying that he supports Free Speech to express that his own speech is being silenced. He is creating an expression of fear to add legitimacy to the second half of the episode. During the second half of the episode, Tucker says that pro-Israel people were trying to keep Tucker away from Charlie by taking away his funding. This devolves into a larger conspiracy theory.
During the last 2 minutes of the episode, he blames the left. He says that Charlie Kirk was anti-war, supported raising wages, supported affordable housing. Then he says that the left is pro-war, pro-death, pro-inequality. Tucker says "the left, the trans community are the shock troops of power". Tucker ends the episode by saying that he loved Charlie Kirk because he opposed the left and transgender people.
Tucker Carlson believes that Free Speech means supporting Kirk and being against transgender people. He believes that criticizing Kirk or supporting transgender people is against Free Speech.