The claim of non-Catholic Christians to be as Catholic as the Catholic Church is nearly as old as Catholicism. Such a claim shows that non-Catholic Christians understand the importance of being Catholic and wish to be acknowledged as Catholics without having to accept the importance of ecclesial submission to the authority of the Roman pontiff. Augustine’s answer to this claim is the classical Catholic rebuttal to the argument:
Although all heretics wish to be styled Catholic, yet if any one ask where is the Catholic place of worship none of them would venture to point out his own conventicle [place of worship] (Contra Epistolam quam vocant Fundamenti 4; source).
Episcopalianism is a transplanted version of the Church of England. The Church of England was formed when Henry VIII took the Anglican church into schism from the universal Catholic Church. Although Henry VIII abhorred the Lutheran heresies, even devoting a book to refuting them while he was still a loyal son of the Catholic Church (earning for himself the royal title “Defender of the Faith” from the pope that Henry’s descendants kept after the schism), it is fair to say that over the centuries the Anglican church and Episcopalianism has adopted some forms and traditions of Protestantism.
While you should not refer to Episcopalianism as “Catholic” because Catholics recognize that the word Catholic has a specific meaning that differs from Episcopalianism, out of courtesy to Episcopalians who dislike the term Protestant you could refer to them as “Episcopalian” rather than “Protestant.”
What “Catholic” Means**