Is it normal to find cigarette butts stuffed inside a wall cavity?

Pull the insulation. Not because the butts themselves are some biohazard, but because fiberglass batts hold odor like crazy and there's no realistic way to clean them. The paper facing especally. You can bag up the affected section, take it out, and stuff in new batts cut to size. It's maybe twenty bucks of material and an hour of work, and you'll kick yourself later if the smell seeps out through the pass-through opening forever. While the cavity is open, wipe down the studs and the back of the adjacent drywall with a damp rag and some basic cleaner. If after that you still catch a stale ashtray smell in the cavity, hit the bare wood with an odor-blocking primer before you close it up. You won't always need it, but if the butts sat there for decades the wood itself can carry some of it. Also check the rest of the cavity while you're in there. Walls from that era are basially time capsules for jobsite trash. Bottlecaps, shims, candy wrappers, cigarette packs, occasionally a whole beer can. If someone was flicking butts into an open wall during one job, odds are decent they were on other jobs in the same house. Pop a light in there and look around before you insulate. As for whether it's common: yeah, more than you'd think. Trades crews rushing to close in a wall will toss anything within arm's reach into the cavity instead of walking it to the bin. Smoke break, wall's open, out of sight out of mind. I've opened up a few walls over the years and there's almost always some archaeology in there. You got a milder version of the surprise, honestly. At least it wasn't a Subway wrapper and half a pee bottle. Once the new insulation is in and the wall is sealed the smell won't travel, so this really is a small fix in the grand scheme of the reno.

Once you get the insulation out and the studs wiped down, the trick is addressing the residual odor in the framing itself. Don't rush to close the wall up. Leave it wide open for at least a few days and run a fan pointed right into the cavity to air it completly dry. I've found that even if the wood looks clean, it will hold onto stale scents. If the smell persists after airing out, I once used a shop vac fitted with a HEPA filter and sprayed the interior framing lightly with a diluted white vinegar solution before replacing the batting and drywall. That got the scent out of the studs before I sealed the room.

I disagree with the idea that the smell won't travel once the wall is sealed up. It's not just about the butts, though. Sometimes the issue is residual odor trapped deep inside the hollow studs, and just swapping the batts doesn't solve that. If the framing itself is carrying scent from old stains or chemical spills, sealing the drywall over it just traps the smell inside your finished space instead of eliminating it. I've had walls that needed a chemical treatment on the wood before I felt confident in the whole project.

I agree that pulling the fiberglass out is the only smart move here. When I did a job where the subfloor smelled like stale cooking, I realized wiping down the wood wasn't enought. I grabbed some white vinegar and coated the exposed studs before putting new insulation back. It seemed weird, but it completely neutralized the scent of old grease and cigarettes. Using that material made the difference for me, beacuse you really need to soak the scent out of the wood itself, not just rinse it off.

I really like the vinegar idea for the framing. It’s simple and usually effective against those deep-seated smells you're worried about. I had a similar situation on a basement project where the concrete slab had absorbed years of old pet smells, so I coated the exposed framing around the pipe penetrations with a mix of vinegar and borax before sealing it up. That combo really helped neutralize the issue completely.