If friction serves as the centripetal force then can it be greater than the centripetal force itself?

Well, I Don't think it's an error, it is just terribly phrased.

It's more like the maximum centripetal force on the object will be the maximum value of static friction.

For angular velocities lower than the max, friction will adjust accordingly.

I think what the book means is "centripetal force $leq$ maximum force of friction".

Think of the simple case of a block on a slightly inclined plane: the maximum force that friction can exert is $mu F_perp$, where $F_perp$ is the component of the block's weight that is perpendicular to the plane; if this maximum force is bigger than the parallel component of the weight (which is trying to make the block slide), then friction will only exert a force equal to the parallel weight, and no more, otherwise the block would start climbing upwards.

So what I think your book means is that, in order not to have skidding, the centripetal force required should be smaller than the maximum force of friction $mu F_perp$.

Friction is reactive force, it is always same as a force that is oposing it. There is of course maximum frictional force and centrifugal force can exceed this so then you have some sliding. Since it has a role of centripetal force in this example these are same forces so to me too this seems strange. That equation up there would make more sense if it compared friction with centrifugal force with condition being that centrifugal must be less than maximal friction.

Static friction will adjust itself (up to a maximum) to whatever value is required to prevent slipping.

Centripetal force is the name given to "a force that acts on a body moving in a circular path and is directed toward the center around which the body is moving". There is no "basic" centripetal force; it is just the name given to a true force- such as gravity or friction- that acts as described in the first sentence. As other answers state, the force of friction must not be exceeded for that force to be a centripetal force.

(A centrifugal force is a fictitious force that appears in a non-inertial rotating coordinate system.)