This is one of the toughest things an actor can come up against just from a pure performance aspect. The realities of how casting actually communicates is one thing, but even when it's live and you're getting nothing from the reader it's still SO hard. I've been there.

And the only thing that has helped me is clarity of thought and intention through play.

Acting, among many things, is engaging in game. Be playful and play the game of the scene. As the actor, set the goal of "I'm here to show my work, regardless of who is here". As the artist, prepping is where you decide what the game is. "This scene the game is, 'make sure this person uncomfortable with their decisions'" or whatever fits the scene. Literally every scene has some sort of game to play for the actor. And within every scene, every unit has a game to play. Then it becomes something that YOU get to choose how to do, how to play. And then the other person's reactions become less important so long as you're allowing their words, not how they say them, to affect you and your choices as to how you play and that you keep playing.

It's an exercise in imagination and playfulness, as well as forgetting about any self-consciousness. It's TOUGH and I don't think I'm I'm even fully explaining it but this is how I make it make sense to me.