The primary reason appears to be cost and availability, as suggested in comments. It's worth noting, however, that in most cases it isn't a flat comparison between lasguns and autoguns of even quality; Chaotic and Genestealer cultists are usually drawn at least partially from the civilian population, so they end up with the (understandably somewhat lower-quality) weapons that are in private ownership. Take this passage from Cain's Last Stand, for instance (emphasis mine):
To my surprise, the answering fire which began to patter off the reassuringly solid rockcrete surrounding us was a hail of lasbolts, rather than the odd mixture of rounds from obsolete firearms and whatever else they'd managed to scavenge that I'd expected, and my palms began to itch even more strongly than before. Something about this situation definitely wasn't right.
Cain's experience leads him to expect that Chaos cultists and such are usually equipped with castoff weapons: old war relics, cheap imports, dangerous homemade guns, and whatever they can loot from their victims. However, renegade Guardsmen like his foes above certainly aren't above using their issue lasguns and other standard weapons.
So the reason that cultists tend to be equipped with autoweapons would seem to be that they are more represented at the low end of Imperial guns, beneath the notice of Guardsmen but all that's available for the poor and disenfranchised citizens who often make up the rank and file of cults. Cheap, low-quality autoguns are plentiful, whereas cheap, low-quality lasguns are less so. It might be worth considering how the lasgun is cheap for the Imperium: in its maintenance, logistics, and operating expenses. An autogun might be more expensive in the long run, but it's likely cheaper up front, and requires less of a technical base to manufacture. For the Munitorum, supplied by forge world tithes and looking to keep kit in active service for decades, lasguns are cheaper. For a drudge worker looking to save up to buy something to ward off muggers, autoguns are cheaper.
Finally, the statistics for autoguns on the tabletop are identical to lasguns for two primary reasons: one is that those autoguns represent military-grade weapons of fair quality, rather than the dregs that cultists use. In both fiction and in other, smaller-scale games (such as the RPGs, or Kill Team) there are a variety of qualities of both auto and lasweapons. It's not that all autoguns and lasguns are equal, it's that you only have the option to equip Guardsmen with autoguns and lasguns at a certain fixed quality. The other reason is of course mechanical. The Strength system is only so fine-grained, after all, and a drop from S3 to S2 would be far too punishing.