Centripetal force for a rotor or centrifugal force?

An rotating object will deform if it isn't resilient enough to provide the required centripetal force.

Take for example the manual skill of spreading out pizza dough by tossing it in the air with a lot of rotation. A wooden disk would keep its shape. The dough does have elasticity (making it tedious to try and spread it out with a roller) but the dough does not have the strength to maintain its shape when it is rotating fast.

There are no exceptions: it is always the structural integrity of the material. The higher the rotation rate that you want to design for, the stronger the material needs to be in order to be able to provide the required centripetal force to sustain the overall co-rotating motion.

Another example: reducing the water content of textile by spinning it in a centrifuge. Adhesion between the fibres of the fabric and the water makes the textile retain water. Spinning the textile in a centrifuge subjects the water to a high G-load. There is not enough adhesive force between the water and the fabric to sustain the circular motion of the water, so rather than co-rotating with the textile the water moves along an outward spiral. This makes the water in the textile move closer to the wall of the centrifuge drum. Eventually the water exits the drum.

Note that in the case of a centrifuge for drying textile the only centrifugal force being exerted is force exerted by the textile on the wall of the drum. That's because the wall of the drum is exerting a centripetal force upon the textile. These opposing forces are not in equilibrium; there is a surplus of centripetal force, sustaining the circular motion. The structural integrity of the drum wall is sufficient to provide all the required centripetal force.

Later edit:
Another example:
the tires on dragster cars are designed to be very, very elastic. When the run starts the fast spinning tires undergo elastic deformation. The diameter of the tire expands until the tension force along the circumference is so large that it provides the required centripetal force. At the end of the run the tire spins down again, and in this phase there is a surplus of centripetal force, causing the tire to contract again. This is the counterpart of the expansion process: when the exerted centripetal force is larger than the required centripetal the rotating object will contract.

Note that in the case of elastic deformation there is a self-adjusting process going on. As an elastic material is stretched the elastic force increases. During spin-down: as the rotating object contracts the elastic force decreases again. Due to the self-adjusting character of the process the actually exerted centripetal force will always be close to the required centripetal force.

Incidentally, the pizza dough undergoes mainly plastic deformation. That is, when the rotation of the tossed pizza dough is stopped tt contracts back a little, but most of the stretching is permanent.