Twitter did not refuse their platform to a conservative writer. He had been using Twitter for years.

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.