The justification is obvious. limiting that power was the will and intent of the founders who were concerned with abuse of the powers they were granting to the government they were creating. If they had been concerned about censorship in the privately owned papers and cyclicals of the day they certainly could have addressed that concern. The obvious difference between government powers and those of private individuals and organizations is that the government can force you to comply with their laws, and the founders clearly intended to give the government the power to enforce. Private citizens and entities, on the other hand can not force you to patronize their services or products, can not penalize you for breaking their terms of service other than to withdraw them from you, which is and should be their right.
What about equal access civil rights you ask? The congress has decided and the SCOTUS has affirmed that if you offer a service to the general public then you can't deny some of them access on the basis of ethnic, religious, or sexual status.
Media companies didn't revoke trump's accounts because he was a Republican, or because he was a white non-Christian, or because he was a man. They revoked his accounts because he insisted on posting false claims about the election that had incited riot and violence...their call, not the government's.
You can't sue Fox News for refusing to air your debunking of their many false election claims. It's their venue and their choice. On the other hand if you are Dominion you CAN sue them for airing false claims about the security of your voting machines, though you do have to prove that they knew or should have known that their claims were false and aired anyway, either out of malice or a blatant disregard for the truth. On the other hand the government has a VERY steep 1st amendment hill to climb to bring federal charges against them for their lies.