The Amazon response to Parler gives a good overview of the "conservative voices" being silenced.
https://cdn.arstechnica.net/wp-content/uploads/2021/01/gov.uscourts.wawd_.294664.10.0_1.pdf
And good riddance to them tbh.
It seems pretty straightforward.
There is no legal basis in AWS’s customer agreements or otherwise to compel AWS to host content of this nature.
I can't see Parler winning this lawsuit.