I am absolutely shocked that a discussion about the definition of "true royalty" has produced several pages of posts without "anointing" being mentioned!!!
To put it in context:
The early Germanic (and many other pagan) kings combined three roles:
Warrior: Not just any warrior, but a military commander, of course.
Judge: In an age that relied upon customary law, being a judge also meant being a sort of legislator, as a judge interpreted the law. In its widest sense it meant presiding over the legislative-judicial assembly of free men. This was also the body that chose the king from representatives of certain divine or sacred royal lines. The office could pass from father to son, but capability, being a strong leader, a skilled warrior, was more important than direct succession.
Priest: These were sacred kings, who either claimed to be gods or demi-gods themselves or at least descended from the gods. They performed sacrifices on behalf of their peoples and were sometimes sacrificed themselves, if the people thought the gods were mad at their kings.
With the introduction of Christianity the role as priest fell away, as the Church had its own priesthood. So did claimed descent from God, as that would be a blasphemy in Christianity. (The Jesus ancestry claimed for the Merovingians in the Holy Blood, Holy Grail legend could be seen as an interesting transitory phenomena between paganism and true Christianity.) Instead many contended themselves with claimed ancestry from King David. Going further back was not much use, as all their subjects were descendants of Adam and Noah too.
What came instead was also inspired by King David: The anointing - becoming God's anointed. While the actual crowning can be seen as the more secular part of the coronation, the anointing was the sacred part, which set the King apart from his subjects and gave him a special bond with God. To acclaim, choose or elect a king and render homage to him was something temporal which the people in whatever forms (councils of the realm, estates, diets, parliaments etc.) did, often in return for oaths in which the king swore to obey their laws, render them justice and protect them against their enemies (NB judge and warrior!). But the anointing was something sacred which the Church administered as representative of God on Earth. Though in reality often too in return for certain promises...
What exactly it meant to be "God's anointed" and the derived "King by the Grace of God" was of course something Kings and the Church argued endlessly about, from the medieval Investiture Controversy right through the absolutist monarch's claim to be answerable to none but God alone. But it is this anointing that gives kingship its sacredness or magic in a Christian context. Blood itself should have no place in a Christian context, that is a wordly or pagan concept. Currently only the British sovereign is anointed. Perhaps it can be argued that the Norwegian monarchs are semi-anointed, since they have special benediction ceremony in the coronation cathedral.
Apart from the mere political considerations, this is no doubt why less than blue-blooded people like Pepin the Short, Gustav Vasa, Mikhail Fyodorovich Romanov and Jean-Baptiste Bernadotte so easily were accepted by their subjects as kings. They became God's anointed. Period.
Bloodlines cannot transfer this sacred magic in a Christian context. Bloodlines can only transfer a claim. A claim to "royal status" is too pagan, I would say. I will interpret this as the claim to the kingdom as the allodial inheritance of its founder. Because after all modern kingship relates to a territory, not a people, as in ancient, pagan times.
I think it's helpful to differentiate between what is royal, that is relating to a king, and what is princely. All descendants of kings can claim to be princely, as can all dynasties that have once tasted kingship or sovereignty. Hence all the Rurikid princes in Russia. And all the princely families in Germany, who were co-sovereigns of the Emperor through the Imperial Diet.
Being princely means that once has a claim to royalty or sovereignty, not that one actually is royal. Yes, all deposed (anointed) kings are God's anointed for the rest of their lives, naturally, but their children, mere pretenders, are just princes and not yet royal. In German usage all the persons with such princely status are grouped together as Hochadel, High Nobility, not as royalty. That seems to me more correct than calling any prince of the (diluted) blood "royal".
Since we are on an imperial site, something should be said about emperors too. But since the case of emperors differ so widely, from elected/acclaimed/self-proclaimed ones like Augustus, Peter the Great and Napoleon, via God's anointed who were the equivalents of the Pope and champions of Christianity like Charlemagne and Barbarossa, to emperors in name and form only (Second German Empire and Austria) and to hereditary, autocratic Emperors (Russia) it really is hard to say anything universal about the imperial dignity. Just that an anointed emperor is God's anointed in the same way as a king and that the notion of an imperial bloodline is even more absurd than a royal bloodline, as there were no pagan imperial bloodlines in Antiquity.