I'm not generally in favor of taking corporate personhood to logical extremes, but I'm kind of OK with companies having values and being able promote those values. Being able to promote some speech over others is part of that.
The First Amendment applies to the government because the government is a privileged party. Its role in society is dislike that of any private citizen or enterprise, and the restrictions we place on it reflect that uniqueness. It only makes sense to extend the First Amendment to other parties that have a unique role.
Which we do, e.g. Common Carrier restrictions on the movement of goods, and a variety of special requirements on telecommunications companies. If we want to say that social media platforms have become a core aspect of modern democracy and need to be regulated as such, there's an argument to be made. But applying it to private businesses in general is overreach in my opinion.
There's another line of reasoning that "First Amendment" is a stand-in for the societal value of freedom of speech. While it doesn't legally apply, we invoke it to mean that freedom of speech is the first-est of amendments, i.e. is the freedom that we rank more highly than any others. This still gets into the same paradox though. A company shouldn't be forced to equally support all viewpoints because then it's not a freedom, but we can certainly express dissatisfaction that a private party is acting in a way counter to the values of our society.
