We have to distinguish that this is a theory of Father Ripperger, not the teaching of the Church; it is only his own personal interpretation.
A father can still utter words of prayer for the protection of his adopted children against evil spirits because he can still be a true father. St. Joseph was not Jesus' biological father, but our Lord still considered his foster father, his legal father.
So, I think, under the law, parents of adopted children still have authority over them.