1) He's not banned for being a conservative, nor writer. 2) They (likely) did not order a cake with writing on it targetting someone. They just wanted a cake for themselves. IANAL, but I'm assuming the bakery got ruled against on grounds of bias crimes against sexual orientation.

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.

Gays can't decide whether or not to be gay, just as people can't decide the color of their skin. The US values protecting people against discrimination based on unalterable traits.

Making intentionally inflammatory comments on Twitter is alterable, so it's not analogous to being gay.

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.