I would be planning to replace as much of the cast iron pipe as possible as a planned repair/renovation when the disruption will be acceptable.
Since it has worked for 80 years it should continue to work if the existing parts are replaced with PVC. You probably don't want to get into upgrades to current codes if that requires new venting arrangements. You might upgrade sizes, such as going to 2" for showers and washing machines, but you don't want to start making new pathways through walls and roof.
It will probably be necessary to remove some wall finishes to remove and replace the pipe.
the drain from the shower looks fine, it's the smaller pipe in front of the larger one in the pics.
this is the only pipe that is messed up, the kitchen has PVC that is spliced into another cast iron pipe, and the washing machine is in the basement and I just spliced it into the basement sink drain.
the pipe behind the walls is what I'm worried about, since I can't see it, and my walls are also original 1928, probably with an undercoat of lead paint, and I have two kids under 3.....