I'm seeing this orange material within the windows of Columbia shuttles -- any thoughts on its precise function? The ISS's Cupola also contains similar international orange bands, though they seem less fabric-y there.
I can address "its precise function" although I don't know exactly what it was made of.
The pressurized crew compartment aka "crew module" of the shuttle Orbiter was a separate structure inside the outer hull, as seen in this diagram.
The Orbiter windows consisted of a rather complex system with the outer, thermal panes mounted on the outer hull, and the two inner, pressure panes mounted on the crew compartment.
The orange material you point out was a flexible joint aka "environmental barrier" connecting the thermal pane with the outer pressure aka "redundant" pane, as shown in this diagram.
The flex joint was needed because there was a "window cavity conditioning system (WCCS)" that helped keep the windows clear. There were also prelaunch nitrogen purges of the cavity.
A closer-up sketch of the WCCS interface to the flex seal.
(I added the blue arrows and the red text)
Systems Training handout "Window Pane Failure Training"