Who I would vote for would be, for example, the third-party candidate I'm actually voting for.

The democrats can't be "shamed" into doing the right thing. They might be able to be pressured into doing it, and establishing a credible threat that you'll withhold your vote if they do something unconcionable is one way of exerting that pressure. They have exactly zero interest in the concerns of people whose votes are guaranteed.

And if they are completely unresponsive regardless, then the only hope of having our concerns listened to is to unseat them, by means of a third party. No matter how unlikely or how long it takes, it's still more likely than the possibility that Biden randomly starts caring about Palestinians out of the kindness of his heart.