Thats not a bad idea .. I just think my birds wouldn't dare go through if something is covering it ... chickens smile
My pop-door is actually a modified 'large dog' doggie door........and it came with the heavy vinyl flap already attached.
I almost removed this solid flap, thinking 'my' chickens would never actually go thru it either!
But I thought it would be a good fly deterrent, and also a good windbreak (vs a wide open pop-door.)
Sooooooooo, I made 4 vertical slits in the vinyl, making 5 vertical blind-type pieces out of the formally solid flap.
Then I used heavy rubber bands and bunched 3 of the smaller flaps together pulled to one side, and 2 on the other......
making an opening for them to pass thru, with the temporarily tied-back pieces, 'without' them having to push past anything.
Then each week I made it a little more difficult for them by undoing one of the 5 pieces........and before they knew it, they were passing thru the slit vinyl flaps, which were now all hanging down vertically!
Worked like a charm, and they have no problem passing in or out thru the curtain of vinyl.
Good chickens!!!