Imagine if you're on Twitter and you can follow a person on Parler. Parler has a right to moderate their own private space however they want. Twitter has a right to moderate their space however they want. But - Twitter can't influence how others moderate their spaces.
So let's say that you are on Twitter and follow Trump on Twitter. Twitter decides to ban Trump. Trump should be able to migrate his account (with the username and profile history) to Parler and you, using Twitter would still magically follow him as before and would be able to read what he posts in your Twitter feed. Twitter would still be able to not show his tweets in their search, or their trending topics or any proprietary feature of the service, but if someone follows him explicitly, they'd still see his tweets in their timeline.