5V shield only ruins your day if you power it from 5V.
So power it from 3.3V instead and all is honky-dory.
Now we have the reverse problem to a short time ago. Previously, some vendors were selling
shields, like for XBee and SD cards, that did not have 5V-to-3.3V level-shifters on them, and
people were blowing up the XBees and SD Cards. So, the vendors finally came around to
redesigning the shields better.
So, maybe the shields should have the 5V vs 3.3V option, then the DUE is safe. Can of worms.