But honest question, what is the difference between a private business refusing to bake a wedding cake for a gay wedding (which courts have ruled illegal), and twitter refusing their platform to a conservative writer.
He's not targetted for either being gay or conservative or any other personal trait other than on their service portraying a seemingly vile human being through targetted harassment of other user(s), which they deemed a breach of their ToS.
Making intentionally inflammatory comments on Twitter is alterable, so it's not analogous to being gay.
What happened is that he used their platform to post impersonating tweets of other users, as well as lead large harassment campaigns against other users. Both are against the Twitter ToS. After repeated ToS violations, he was finally banned.
So no, they did not refuse their platform to a conservative writer. They did not do anything to anyone for their political beliefs. They kicked off a user who had repeatedly broken the rules.