You are I think mixing categories? If a given business, or corporations, in any way shape or form indicate that they oppose any Constitutional right, through any means at their disposal, they must be taken to task for this.
They are obligated to remove 'hate speech' and other expressions and to do this reasonably. They may have an obligation to limit some speech but not *as they see fit*. The line is drawn when a broadcaster engages in editing and thus becomes a 'publisher'. But I assume you know this.
Free speech and the Second Amendment are certainly under threat. In America, obviously, it has already become *illegal* to say and think certain things publically. You know this and we all know this. Let's make it conscious.
Banning, shunning, demonetizing, no-fly lists (there are some who propose these) and any activities that curtain the First Amendment right must be quickly opposed. These are its manifestations. You might be in favor of this and support it, but I do not think this is a defensible position.
While I respect your view, and there is a certain logic in what you say (about a private business having the right to control speech), you must surely be aware that the social media platforms like Twitter and Facebook have become, and have been transformed into, areas that are comparable to and commensurate with 'the public square'.
Obviously -- and in a *democracy* -- the public square and the sphere of public, civic communication, is a special and a crucial area. I assume that you recognize this, though you might not want to concede the point.
By your (apparent) definition Google could limit any speech it does not like from flowing through it. Obviously this is a totally indefensible position, but try to defend it if you think you can.