Their shareholders are already panic selling (FRC down 36%), their bonds appear to be sinking, and few private parties wants to throw good money after bad. When you have to put out an emergency statement to reassure everyone of your creditworthiness, it's already gone.
I do agree that First Republic is in a much better situation relatively to SVB, but illiquidity and insolvency risk is real. I don't really see a reason why any business or individual with more than $250K shouldn't be wiring funds out ASAP, unless you're feeling extra charitable and want to be the bail-in to those who run before you.
There is nothing to lose, other than setting up new accounts.