I have a small van, extremely longhaired fluffy cat, blackout curtains, and do not have this problem. Kitty hair sticks to some fabrics but not others.
I think you need a different blackout fabric.
I wish I could tell you what kind mine is -- especially since I want to get more of it for my new van! All I can say is, it was Eclipse brand, from Walmart.com, came in multiple colors, and has a slightly nubby texture to the fabric side (white plastic on the back, which I too cover with fabric.
I do put my curtains in the wash about twice a year.