There is no free speech issue here, Twitter isn't operated by the government, neither is Facebook or Reddit. My point is, people are still free to set up their own servers at home, running their own app, their liberty to do that is not harmed by Twitter rejecting content. On the contrary, it's an opportunity for free speech advocates to remember that.
One has never been able to compel a publisher to publish them.
You may have a different concept, but to my way way of thinking that has always been the connection between the First Amendment and Free Speech.
But, since you asked, businesses that offer services to the public can refuse service to anyone UNLESS they're refusing a member of a protected class, for being a member of a protected class.
White restaurant owner kicking out a black lady because she's belligerent/drunk/whatever -- fine.
White restaurant owner kicking out a black lady because she's black -- not fine.
Religious bakery owner refusing service because it's Monday -- fine.
Religious bakery owner refusing service because the customer is gay -- not fine.
But again, please no more whataboutism.
In all contexts, freedom of speech is considered a 'right', but in some contexts it's a positive right, and in others it's a negative right.
In the US constitution, it's a negative right. The First Amendment states that 'Congress shall write no law ... abridging the freedom of speech.' In the Universal Declaration of Human Rights, it's a positive right:
"everyone shall have the right to freedom of expression; this right shall include freedom to seek, receive and impart information and ideas of all kinds, regardless of frontiers, either orally, in writing or in print, in the form of art, or through any other media of his choice". [1]
To dissallow Twitter to shape its own content/user base strategy would be unethical.