Good luck with your demand.
Do you have a Constitutional principle to back it up?
I do. Two in fact.
The intent of the founders is to prevent censorship of speech. Their belief was that the threat to freedom of speech would emanate from government, but it is clear to me that they would have objected to it just as strenuously if they had considered this threat to have possibly come from any other source.
There is also this principle of Eminent domain. If the public need for something is sufficient, private property can be commandeered for public use.
I believe the public need to have uncensored communications wherever large numbers of the public go to communicate, is so crucial to our system of governance, that we must use the power of eminent domain to force large communications companies to carry all traffic.
There is a third point that is only indirectly a constitutional point, but very directly a practical point.
If private corporations are permitted to censor speech, then how are we to prevent government from quietly pressuring them behind the scenes to do the government's bidding?
Remember that Youtube video the Obama government pressured youtube into removing? (the one made by that guy who was the scapegoat for the Benghazi fiasco.)
When government need merely pick up a phone and tell a company they don't like some particular "speech", how many companies will tell them to go F*** themselves?
Make it public law that they cannot censor, and the government can't apply behind the scenes pressure to get them to do it.