Is carbon dioxide soluble in petroleum ether, and why?
Carbon dioxide is, in fact, more soluble in nonpolar solvents than in water.

From the Wikipedia page on carbon dioxide: Solubility in water
1.45 g/L at 25 °C (77 °F), 100 kPa
(Alternative source: CRC handbook. Solubility is about twice as much at 0°C.)

From IUPAC, Solubility Data Series: Carbon Dioxide in Non-Aqueous Solvents at Pressures Less Than 200 kPa, chart on page 3: mole fraction of CO2 in hexane at 101.3 kPa, 300 K = 0.012, which corresponds to 4 g/L.
(Solubility is only slightly (10-20%) higher at 0°C.)

So the forum posts I read were wrong.

As to why, I suppose it's sufficient to argue that CO2 is a nonpolar molecule, and like dissolves like.
(It's true because it's Latin: Similia similibus solvuntur! )