Up until about a month ago, I thought any piece of wood that felt light and airy needed to be stabilized. After trying to stabilized some of those in question, I found out I was wrong. For example, I had a really pretty Redwood burl blank, but it weighed just about what a piece of Balsa its size would. I just knew if I tried to turn it without stabilizing it, I'd ruin it. I was dead wrong. I attempted to stabilize it, but it wouldn't absorb any of the stabilizing solution... surface only. I was utterly perplexed and amazed, so I decided to turn it anyway. It turned easily and without incident. By the same token, I cut into some spalted Maple almost a year ago and it wasn't punky or soft or light. I thought I could turn it without any problems... WRONG. Even using half a bottle of CA on a pen blank barely got the job done. Stabilization is in order for that stuff for sure. I have and do turn spalted Beech w/o stabilizing and have no problems, but most other spalted woods I will at least attempt to stabilize before turning.
The rest is trial and error... with a significant amount of the latter. For me anyway.