My opinion isn’t binding and I haven’t developed a position; more to the point, if they were a common carrier, I don’t see how their terms of service and code of conduct would not be applicable all the same. Common carriers can still refuse service to specific offending individuals if not the government as collective entity, for no reason, or for cause, such as violations of company policy or terms of service.
Twitter is a private company, which uses private servers and network switches, that communicates with ISPs and their private equipment, to send the information we're talking about.
Radio and TV use public resources (EM waves), to which they have been granted a government license, to transmit information, so the government can ask them to do certain things at times.
Most phone companies (and cables) were granted local monopolies that allowed them to build out infrastructure and amortized the cost over decades. (Actually, in the US, there was only a phone company for a long time: AT&T.)
Twitter, Facebook, Reddit and so on are following (or being pushed for political reasons) down the traditional slippery slope where first they ban child porn, KKK recruiters, anarchist groups exchanging bomb-making instructions and people openly selling illegal drugs.
Then things get broadened because yes, that is copyrighted stuff being shared, guess we should stop that. Yes, if that revenge porn isn't illegal it will be soon, guess we should block that. Yes, if they literally chose a nazi flag as their logo we can agree they're a hate group. Yes, that user's post about the smooth taste of Lucky Strike cigarettes does look like it was upvoted by a botnet. Yes, we could probably detect those rape threat messages you received and block them, senator.
And before you know it, you're adjudicating whether that person was joking when he said he'd blow up the airport for cancelling his flight; whether that 'parody news' website claiming vaccines cause autism is clearly enough a parody; and whether the letter Q is a hate symbol.
Guys in suits getting interviewed on cable news wear Q lapel pins for a reason. It’s to show the 8channers that they’re part of the in-group. Just like Trump tweeting a doctored CNN chyron on top of a doctored Carpe Donktum video. Propaganda and dog whistles can be obvious; placebo effects still work even in cases where you know it’s a placebo.