Most carbon fiber you might see in the world is sealed with resin. But under that resin, it's just sheets of woven or non-carbon fiber fabric. And those fibers are just nanometers thick and can easily puncture cell walls the same way as asbestos.

I used to work in a ski shop and we would regularly cut down carbon fiber ski poles using a band saw. I think we used a mask... Hopefully

Every resin-based material is friable after the resin decays. That's one of the major problems with asbestos roofs, the resin holding the asbestos is breaking down after decades of sunlight.

That's the other thing, too. It's rare to be in a situation where you could inhale it. The only example I can think, which is also a rare situation, is if a vehicle that uses it is involved in some kind of accident and breaks the piece of carbon fiber. That could release it into the air causing you to breathe it in.