I've had both stabilized and not stabilized wood move in Montana and here in Michigan with just the changing of the seasons. Montana was very dry and Michigan is humid in the summer and dry in the winter.
I have a kitchen knife with ironwood scales. Every winter, it shrinks up and you can feel the pins and catch your thumbnail on the edge of the tang. Every summer it swells slightly and the pins are flush and you can't catch the tang with your thumbnail.
The movement is VERY slight, so we're not talking huge amounts here. Stabilized wood is the same way. But it gets presented all the time that stabilized wood is 100% sealed and WILL NOT move. That's just not true. I've had stabilized wood warp, several times. Buckeye burl, redwood burl, amboyna burl, maple burl, spalted maple. I've had all of these move on me. And I'm VERY careful working it as far as temperature and introducing stresses to it via machining. All of it was stabilized and all of it can move with moisture changes. Not a lot but enough to notice and shoot the theory professed by some that stabilized wood is sealed and impervious to moisture and movement.
Amboyna is one wood where in my experiences, stabilizing did more harm than good. Professionally stabilized, and cut from the same big block side by side, I had one block stabilized and one not. The stabilized block came back all full of checks and cracks and bowed quite badly. I milled it flat and left it sit for two months. It continued to crack and check. The unstabilized block is going strong to this day. moisture on both was 6-8% before stabilizing.
African blackwood is the only wood that I've never noticed any type of movement. I'd be interesting if some of you guys tried this and reported your findings. Make some scales, get them dead flat. Scales that are truly flat will almost stick together from vacuum pressure when you press them together. You can feel it. Anyway, make some scales, get them dead flat and then let them sit for a month or two and see if they're still dead flat. I bet most would notice some slight warp or curl. Not much mind you, and good epoxy and pins would hold them forever....but most will have moved slightly I'm betting.
I will say that I use stabilized wood quite a bit. But a lot of it is because that's what the market really demands, not because I think it really needs it. There is no doubt that stabilizing adds some weight to the wood and in some woods, like redwood and buckeye for example, it makes a seemingly noticeable difference in surface hardness. I'm not sure it really makes it that much more 'stable' as I still maintain that wood being dry and seasoned is what has the largest effect on it's stability.
But stabilizing is relatively new. Look at all the weapons they've unearthed that had wood handles still largely intact after spending a hundred years or more in many cases underground. You can't tell me a wood handle that's not stabilized is going to twist and warp and fall apart in a matter of a few months or even a few years. Use something suitable, not pine or green willow, and finish it properly and take care of it and it will last a lifetime.
Just my two cents relating my experiences with all woods, stabilized or not.