Lutheran Catholics are not Catholics. The Catholic Apostolic Church is not part of the Catholic Church, despite its name. To be Catholic means to be in communion with the Bishop of Rome and to submit to the Church's authority. Catholics must accept all the dogmas and doctrine of the Church, without exception. That's what makes the Church "catholic," which means universal. The same teachings are accepted by those in the Latin Rite, Byzantine Rite, Coptic Rite, Syriac Rites, etc.
Those "Catholics" who reject Church dogmas and doctrine, such as prohibition on the use of contraception or divorce, are not Catholics in good standing. They are in defiance of fundamental, infallible, non-negotiable Church teaching. Those Catholics may not receive the Eucharist.
Well now you are simply equivocating, or are those Catholics who claim to be such, but who stand in opposition to certain dogmas? Luther formed his church based directly on he Catholic church, but with the elimination of the practice of selling absolution, which, by the way, is no longer practiced by the Catholic church "proper" or orthodoxy(ie Roman Catholics). The Lutheran church is Catholic in all other regards, and Apostolics hold high regard for the leaders of the church proper.
The Apostolic Catholic church is Catholic, with minor modification, and holds the intended purpose of reuniting the western Roman Catholic, with the eastern Orthodox Catholic churches to for a unified singular Catholic church.
But, the thing that makes all of these churches Catholic is not to be found in their universal and absolute acceptance of dogma, doctrine and creed. But in that they all hold the same origins and are often referred to in the Nicene Creed.
What we see when we observe all these differentiations along with the original motivating factors is what amounts to an evolution taking place within the Church in only a few scant generations, till it becomes different enough that they are no longer truly compatible.
Of course, those that are incompatible, in this case, are often a matter of perspective... suggesting that they are not truly incompatible, but stubbornly avoiding intermingling, except in their common outrage(for instance, their united front against all things agnostic/atheistic).
But, all Christianity gets its birth, originally in Judaism with the Prophecies of a savior(Greek, Christos). That's right all you Christians out there... The name of your religion gets its name from Greek Orthodoxy, not from an actual last name of some character.
The main point being that this dishonest approach of yours is entirely unnecessary. Especially since it really doesn't make two shits a difference as to what Christians consider themselves Catholic, Apostolic, Lutheran, Protestant, etc. Christian is Christian, for the most part. Although, I will confess that there is a HUGE difference between those who take the Bible as 100% literal truth, and those who are far more moderate in their approach... accepting that large(vast majority) portions of the Bible are allegorical.
When I speak as an atheist, I am typically speaking about, or to those who are evangelical fundamentalists(proselytizing Biblical literalists). But, philosophically speaking, there is a lot to be said to and about allegories as well.