I have an expr which has List at various levels and I want to display them nicely as a column inside a frame but my problem is that the search for List goes inside things like DateObject to ruin their structure.

Replace[
    expr,
    x_List/;!MatchQ[...[...x...],DateObject[x,__]]:>Framed[Column@x]
    All
]

So how should I define such a Rule?

sample expr:

{1->a,2->b,3->c,4->{5->d,6->e,7->Today},8->Yesterday,9->{10->f,11->{12->Tomorrow,13->g}}}