It seems plausible that a cloth bag requires a comparable amount of petrochemicals to make than a plastic bag, agriculture is quite fuel intensive and uses a bunch of other nasty chemicals in large amounts, while a few grams of plastic require just a few grams of oil - for me it's hard to tell whether growing sufficient cotton for a single bag (which is quite a bunch of cotton plants) can be done with a few grams of fuel.
Thankfully, this is studied by experts for their entire lives and we don’t have to learn the answers by speculating on Hacker News.
I’ll note that what you’re comparing petroleum based manufacturing to is the most pointlessly intensively harmful and wasteful form of agriculture – growing conventional cotton.