The question surely strikes most people as utterly nonsensical, for if Lutherans AREN'T Protestants, then who is? But it is a useful question for clarifying what is meant by "Protestant." And I'd suggest that - setting aside for the moment the Western Rite Orthodox - the simplest answer is this: Protestants are Western Christians who reject the claims of the Bishop of Rome to be the universal bishop of the Church, the divinely-appointed head of all Christians. If THAT is the definition, then, indeed Lutherans are Protestants, and we can wear the name without any sense of dishonor, for it does not imply in any way the revocation of our catholic heritage.
Sadly, though, in most folks ears I suspect that "Protestant" equates rather to something else, of which the Reformed (of whatever stripe) tend to be the epitome. Lutherans, to their eyes, seem to be but quasi-Reformed. Almost, but not quite there. Luther they pay homage to, but honestly believe that his conservative tendencies got in the way of a thorough-going Reformation and in fact ended up tragically and needlessly splintering the Reformation movement.
The key is always to ask how a person understands the term. Lutherans most certainly ARE Protestants vis a vis the papal claims. But we see that position of protest in no way as undercutting our commitment to a truly catholic heritage; rather, it is mandated BY that heritage. Dr. Secker relates how when Dr. Piepkorn heard of some Lutherans converting to Rome, he remarked that he would march to the gates of Rome and plant his banner. He was convinced, utterly convinced, that the key to fidelity to the catholic heritage was embracing the Lutheran Reformation. For here he found the faith of the Fathers and a catholicity whose supreme mark was adherence to the Gospel of Jesus Christ, the only Savior of sinners, as witnessed by the infallible Word of God, the Sacred Scriptures.
If anyone asks me if I'm a Protestant, I don't hesitate anymore to answer: "Indeed I am. But maybe a Protestant is something different than what you are thinking! For I am an original Protestant. That means, I am one who believes that Baptism is for infants and adults and through it the Blessed Trinity saves us; I am a Protestant who believes that in the Eucharist Christ gives me to eat and drink His most holy body and blood beneath the appearance of bread and wine; I am a Protestant who believes that the words of Christ's called servants release me from sin, forgive me, and open wide the gates of heaven; I am a Protestant who believes that the Eucharist is the beating heart of the Church's life; I am a Protestant who rejoices in the liturgy of the Mass and the Daily Office; I am a Protestant who acknowledges the Office of the Holy Ministry as divinely established and ordained for the salvation of our souls. Please don't call me 'high church' or 'hyper confessional.' Just call me Lutheran. For that's what I am."