Correction: the Act of Succession to which I referred in my last post was that of 1702, not 1712.
The current Grand Duke of Luxembourg, Henry, is descended from the royalty of Belgium (Saxe-Coburg), Portugal (de Braganca), Spain (Bourbon), France (also Bourbon), Austria (Hapsburg), Sweden (Bernadotte), and Denmark (Schleswig-Holstein). So he is related to, but not descended from, the Princes of Liechtenstein (via Hapsburgs) and the British royals (via Saxe-Coburg). Some of his bloodlines may descend from earlier British/English royalty; but if I try to figure that out, I’ll be here all day!
I’m not sure what you mean by the Greek Orthodox Church being ‘older’ than the Roman Catholic Church…
I’m not hugely familar with contemporary Anglican ecclesiology, but traditionally there would be a tradition within the Anglican Church (described normally as ‘Anglo-Catholic’ or ‘High Church’) that would seek to describe the Anglican Church as part of the ‘Catholic (as in Universal) Church’… Concequently, the Orthodox Churches of the East, would seem like kindred to them, being National Churches, professing a belief in the ‘Catholic Church’ (but interpreting it more broadly than just the Roman Catholic Church) and being somewhat estranged from Rome. Indeed, I suspect that in the mid/late 1800’s some kind of Ecumenical attempt was made for the Orthodox and Anglican Churches to mutually recognise eachother, though I believe no substantive agreement was reached. (This would cause obvious difficulties for the more Protestant/Low Church Anglicans at the time who would probably see in Orthodoxy even worse ‘corruption’ [to their way of thinking] than in the Roman Catholic Church.)
It makes a certain kind of sense that Roman Catholics not be allowed become spouses to the English Monarch. Afterall, the English Monach claims to be ‘Head of the Church in England,’ a claim that runs contrary to the Papacy’s claim to be head of the Universal Church. To the best of my knowledge, the Patriarch of the Greek Orthodox church has never tried to claim any authority over the Church in England.