Hi again. I was waiting a few days to see if someone with more expertise was going to chime in. But perhaps others don't recognize the issue, either.
It doesn't seem like there is anything amiss with the care regimen or the conditions. I don't think any minor oversight in care is causing this. Thanksgiving cactus is a tough plant...my mother has a monstrous one that has to be coming up on 30 years old, and it has spent most of its life in a semi-dark corner, in pots without drainage holes and with massive rings of salt buildup all around it.
She's done almost everything 'wrong' and somehow it just shrugs and keeps pushing out wave after wave of blooms every year.
I've also seen some sad specimens at my local car dealership that are always bone-dry and almost completely red from the tips down to the soil, and yet these are somehow still surviving. I am no expert but this leads me to suspect your cactus might have an actual disease, and not just blemishes from some lapse or other in care. I would isolate it from other plants, if you haven't already.
The only other thing I can think of might be something like cold damage, if e.g. a window was opened and a blast of freezing air got to it. But you say it lives next to an unaffected plant, so that sounds unlikely.
Taking another look at the photo...it looks like there are segments that don't have mottling on them. You could consider amputating the affected segments and seeing if that stops the spread.
On the other hand, if you do have sections of plant free of mottling, the plant may well recover quickly from even extensive amputation. If the root system is intact, Schlumbergeras can recover well from pretty severe pruning.
