It depends what you mean by 'white chocolate'. Most white chocolate can still be dangerous as it contains cocoa butter, but the toxins (theobromine and caffeine) are at minuscule levels compared to products containing cocoa mass/powder (ie other chocolate).
Additionally some so-called white chocolate nowadays actually does not contain any cocoa butter, or when it does it only has small amounts. Much 'white chocolate' is just milk and sugar. Neither of these are toxic for a bird, but they also aren't that healthy - if they eat much of this they could get quite an upset stomach.
So the answer is 'it depends'. But white chocolate is not nearly as dangerous as dark varieties, in fact some types of white chocolate could be perfectly safe.... but why bother as they would not be healthy anyways?