What they mean to say is that In a split construction such as this one, each part of the construction must be 'slotable' before the following part in a grammatically correct manner. What you have here are two verbs, each made of a helping verb+perpetuate:
has perpetuated is the present perfect form of the verb perpetuated.
will continue to perpetuate is the future simple form+infinitive (to+V) of the same verb.
the problem is that the present perfect form (has+V3) requires "perpetuate" to be in perfect form (perpetuated), while the future simple form /+infinitive requires a base form (perpetuate).
Thus, these two helping verbs (has and will) must each be followed by a different form of "perpetuate".
The correct form of the split construction would be "has perpetuated and will continue to perpetuate", which is awkward, but grammatically correct - each part of the split construction correctly uses its own required form.
