X-Pro1 + Sunglasses = Fail
LCDs use polarization as the switching mechanism. Polarizing sunglasses use polarization to reduce the amount of light, but only letting through light waves with a particular orientation. If that orientation doesn't happen to be the one the LCD is emitting, your going to see next to nothing.
This will be the same for any camera LCD. Your only options are:
Buy a camera with an OLED screen (which does use polarization)
Find a camera that has an LCD the by chance emits the polarization your sunglasses let through
Buy new sunglasses that are don't use polarizing lenses
I'd go for the latter personally, but that's just me!