Why does CO2 diffuse through a butyl rubber membrane more readily than air?
The permeability of a gas through rubber depends mainly on its diffusivity and solubility in rubber.

$\ce{CO2}$ has a significantly higher solubility in rubber than $\ce{O2}$ and $\ce{N2}$, whereas the diffusion coefficients differ not that much.

The result is that carbon dioxide passes ordinary rubber about 5 times faster than oxygen and about 15 times faster than nitrogen[1, 2].