Earlier quoted context omitted.
The big, ostensibly neutral, communications monopolies need their censorship practices heavily regulated. People with private blogs needs to be absolutely free to control commenting however they would like. I believe that we can respect both of these positions easily, 99% of the time, with our court systems deciding on some of the grey in the middle.
Twitter doesn't even remotely have a monopoly on political communications. What counts as a "private" blog? That seems like an arbitrary distinction.
Unlike in the 1800 when everyone could just go the the town square or publish their own pamphlet and have almost equal reach, today most discussion happens in 2-3 outlets: Facebook, Twitter, YouTube, etc.
Whether those started as private companies, whether those are not public goods, etc, should be irrelevant. They have de facto captured a big chunk of the conversation that shapes the public opinion.
I'd argue the same was true for TV and newspapers in the 1900-2000 -- they had a disproportionate power of shaping public opinion, and a monopoly of control on it. That was bad -- and it was already said that "he who controls the mass media, controls democracy". Even if people still had the "first amendment right" to open their own newspaper (as if that's practical), or whatever.
But at the time, at least, newspapers and tv stations had limited pages and run time, expensive production costs, and it was at least reasonable that they couldn't include everybody's voice.
Today, services like Twitter, Facebook, etc, not only have small marginal costs for including another voice, but they encourage and actively want to add more (all) people in their platform. So there's no excuse (from that point) of censoring people.