"It's a private company" has been the excuse for the abusive censorship. Are you saying if someone has right wing leanings on free speech that politicians will now change their tune and threaten it?
But trying to shut down a platform which is considered (by some) "critical infrastructure" might find you in a position where regulations restrict what you can do.
It's not a certainty but a possibility that this might happen (regardless of who is in power at the time.) Many politicians of different leanings use Twitter for communication.