While they might be able to climb a short, low fence, they are unlikely to scale anything tall or particularly vertical.
As for cat doors, skunks are large enough that they could potentially fit through a cat door, depending on the size of the door and the skunk. However, they don't typically use cat doors as they are not domesticated animals and do not have the same needs as cats.
It's important to remember that skunks are wild animals and should not be encouraged to enter your home. If you find a skunk in your yard or near your house, it's best to call a professional wildlife removal service to handle the situation safely.