As to 1st part: Honestly, it doesn't make much logical sense, especially to someone reading the text of the constitution with the expectation of understanding

As to 1st part: Honestly, it doesn't make much logical sense, especially to someone reading the text of the constitution with the expectation of understanding it... but they really wanted a way to make civil rights laws happen. 2nd order effects, good case results in bad caselaw, etc. The net effect is that constitutional protections originally meant only to apply to the federal government have, one at a time, over many years, been ruled as being applicable to both States and private businesses. To the point where it's presumed that most/all federal rights/protections should be applied this way. With guns being a currently battled sort-of exception. (Similarly, read the text of the 8th amendment, and try to figure out the bridges crossed to result in Roe v Wade) Twitter fits in as a business, at least in this context, for the sake of this particular argument. (As opposed to those who want to classify it as a utility, or "public square," etc) Some people get upset at it, but the easy comparison is they're the modern version of the 1960's lunch counter or bus company, but instead of skin color, it's political opinion (or sometimes even religious beliefs, depending on the specific topic of discussion).