The NY Post is old (founded by Alexander Hamilton!) but in recent decades has truly evolved into a gleefully trashy and conservatively opinionated newspaper, having been run by Rupert Murdoch for some time.

I completely fail to see how their rights are somehow being impinged here. They have their own mini-media empire and are part of a larger media empire.

How... exactly are they being stifled and why is Twitter obligated to amplify their voice?

I would certainly agree that this does fall afoul of Section 230, which I think was a great foundation but could use some serious rethinking.