Before getting our leather couch, we had microfibre. The fur will stick to it like a magnet BUT it wipes clean very easily and fur doesn't get stuck in the weave. It also washes well. We used to take the cushions out of ours and throw the in the wash. It never faded and came out looking like new every time.
Also, before ruling out leather completely, have you checked out analine leather? Any scratches can be buffed right out and its very difficult to puncture. Its a thicker yet cheaper grade of leather, so its affordable. Any drool, food, or fur just wiped right off it.