That's one thing to consider, but it's ignoring a major aspect - biodegradability. Yes, a plastic bag is in some ways more efficient per ton than a cloth bag but doesn't decompose safely and fast, cloth usually does.
What's worse, adding some inert foreign molecules to the environment, or adding some CO2, excess nitrates, and excess phosphorous, taking down a bit of native vegetation, and revolving some more soil?
I really don't know the answer, but I bet everybody on the anti-plastic crusade doesn't know either. I would really like if somebody cared to do some unbiased studies on this (not the ones full of flaws reinforcing the author desired answer - whatever that it).
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.
Problem is they're often not inert. The polymers may be, but the bisphenol plasticizers, UV stabilizers, dyes, brominated fire retardants, mold release agents, etc may not be, and they leach out over time.
The molecules I'm speaking of are already reactive. Again it's not just the bulk polymer, there are a bunch of "special ingredients" added to most plastics, plus contaminants introduced during recycling.
Taking oil out of the ground and burning part of it to create plastic out of the other part, and then throwing it away or incinerating it, isn't carbon capture :)
I really don't know the answer, but I bet everybody on the anti-plastic crusade doesn't know either. I would really like if somebody cared to do some unbiased studies on this (not the ones full of flaws reinforcing the author desired answer - whatever that it).