An actor set up a camera and told people to chant a mantra into it. When people started saying political things he didn't like, he flipped his shit, got pushy and ended up getting arrested. When people started saying racist things (which is protected by the constitution) that he didn't like, he moved locations. That sounds a lot like trying to shutdown free speech.
The Constitution doesn't compel private persons to provide a platform for speech they disagree with.
Note that I am not really taking a side on whether the actual theft of the flag was admirable or not here, I just want to make clear that just because it's constitutional for private individuals to do most anything (given that the constitution places almost no restrictions on individuals), that does not mean that the broader concept of freedom of speech only applies to governments.
The point is that the comment I was responding to was painting this as a side A trying to limit the speech of side B. I was trying to say (quite poorly it seems) that this could just as easily be construed as side B trying to limit the speech of side A.